$f$-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Chi Hoi Yip; Semin Yoo; Seoyoung Kim

arxiv: 2503.19603 · v3 · submitted 2025-03-25 · 🧮 math.CO · math.NT

f-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials

Seoyoung Kim , Chi Hoi Yip , Semin Yoo This is my paper

Pith reviewed 2026-05-22 22:46 UTC · model grok-4.3

classification 🧮 math.CO math.NT

keywords Diophantine tuplesquasi-random hypergraphsfinite fieldsmultivariate polynomialsPaley sum hypergraphsasymptotic countingextremal set theory

0 comments

The pith

Quasi-random hypergraphs from multivariate polynomials over finite fields give an asymptotic count of k-Diophantine m-tuples.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds explicit families of quasi-random hypergraphs by evaluating multivariate polynomials over finite fields. These hypergraphs supply a single framework that covers Paley sum hypergraphs as well as those arising from Diophantine tuples and their generalizations. With the new construction the authors obtain a precise asymptotic formula for the number of k-Diophantine m-tuples, which directly answers a question raised by Hammonds et al. The same method is used to examine further questions about f-Diophantine sets and to tighten an older bound of Chung and Graham on even partial octahedrons inside Paley sum hypergraphs.

Core claim

Explicit families of quasi-random hypergraphs constructed from multivariate polynomials over finite fields yield an asymptotic formula for the number of k-Diophantine m-tuples.

What carries the argument

Quasi-random hypergraphs built from multivariate polynomials over finite fields, whose edge-density and discrepancy properties enable asymptotic counting arguments for Diophantine tuples.

If this is right

An explicit asymptotic formula exists for the number of k-Diophantine m-tuples in finite fields.
A single polynomial-based method unifies the study of Paley sum hypergraphs and hypergraphs coming from Diophantine tuples.
Several recent results on f-Diophantine sets are extended and improved.
A classical estimate on even partial octahedrons in Paley sum hypergraphs is sharpened.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same polynomial constructions may supply quasi-random hypergraphs for other enumeration problems that involve polynomial equations over finite fields.
The method could be tested on small fields to verify the error term before attempting larger-scale computations.
If the quasi-randomness persists under composition of polynomials, the framework might handle higher-arity Diophantine conditions.

Load-bearing premise

The polynomial constructions produce hypergraphs that are sufficiently quasi-random for the discrepancy estimates in the counting argument to hold.

What would settle it

A direct count, for small prime powers q, of k-Diophantine m-tuples whose deviation from the predicted main term exceeds the error bound given by the quasi-randomness parameters.

read the original abstract

We investigate $f$-Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi-random hypergraphs but also provides a unified framework for studying various hypergraphs arising from multivariate polynomials over finite fields, including Paley sum hypergraphs, and hypergraphs derived from Diophantine tuples and their generalizations. We derive an asymptotic formula for the number of $k$-Diophantine $m$-tuples, answering a question of Hammonds et al., and study some related questions for $f$-Diophantine sets, extending and improving several recent works. We also sharpen a classical estimate of Chung and Graham on even partial octahedrons in Paley sum hypergraphs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives explicit polynomial constructions for quasi-random hypergraphs over finite fields and uses them to count k-Diophantine m-tuples, resolving a question from Hammonds et al.

read the letter

The main takeaway is that this work builds explicit families of quasi-random hypergraphs from multivariate polynomials and applies a counting lemma to obtain an asymptotic for the number of k-Diophantine m-tuples over finite fields. That directly answers the open question from Hammonds et al. They also place the construction in a unified framework that covers Paley sums and related objects, and they sharpen the Chung-Graham bound on even partial octahedrons in those hypergraphs. The constructions look systematic rather than ad-hoc, which is a practical plus for generating examples in this corner of combinatorial number theory. The argument is framed as responding to an external question rather than a self-referential loop, and the abstract gives no sign of free parameters or invented entities. The soft spot is exactly where the stress-test note flags it: the load-bearing step is proving that the polynomial hypergraphs have the required edge density together with discrepancy small enough for the counting lemma to produce a nontrivial asymptotic. If the character-sum or Fourier estimates used for discrepancy are uniform in the degree and field size, the result holds; any gap there would leave the formula unsupported. The paper claims to establish those bounds, so the referee would need to check the details of those estimates rather than the overall strategy. This is a paper for people already working on Diophantine sets, Paley-type graphs, or hypergraph methods in finite fields. A reader who knows the recent literature on these topics will see the value in the new families and the sharpened estimate. It is not aimed at a broad audience. The work shows clear engagement with the literature and an honest attempt to answer a stated open question, so it deserves a serious referee even if the discrepancy proofs turn out to need tightening.

Referee Report

2 major / 2 minor

Summary. The paper constructs explicit families of quasi-random hypergraphs over finite fields from multivariate polynomials, providing a unified framework that includes Paley sum hypergraphs and those arising from Diophantine tuples. It derives an asymptotic formula for the number of k-Diophantine m-tuples, answering a question of Hammonds et al., studies related questions on f-Diophantine sets, and sharpens Chung-Graham estimates on even partial octahedrons in Paley sum hypergraphs.

Significance. If the discrepancy bounds for the polynomial hypergraphs hold uniformly, the work supplies explicit constructions and a counting lemma application that yields nontrivial asymptotics for Diophantine tuples. This strengthens the toolkit for quasi-random hypergraphs in additive combinatorics over finite fields and extends several recent results with a systematic polynomial method.

major comments (2)

[Construction and quasi-randomness section (likely §3–4)] The load-bearing step is the proof that the multivariate polynomial hypergraphs simultaneously achieve constant edge density and sufficiently small discrepancy for the counting lemma to produce the claimed asymptotic. The manuscript must exhibit the precise character-sum or Fourier estimates establishing the discrepancy bound uniformly in the degree and field size; without these, the application to k-Diophantine m-tuples reduces to an unverified assumption.
[Asymptotic counting argument (likely §5)] The asymptotic formula for the number of k-Diophantine m-tuples is stated to follow from the hypergraph counting argument, but the error term depends on the discrepancy; the paper should make explicit how the o(1) discrepancy translates into the error term in the final count, including dependence on m, k, and q.

minor comments (2)

[Introduction] Notation for the polynomial degree, the parameter f, and the tuple size m should be introduced with a single consistent definition early in the paper to avoid later ambiguity.
[Paley sum hypergraphs section] The sharpening of the Chung-Graham estimate on even partial octahedrons should include a direct comparison table or statement of the previous versus new error term.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting the significance of the polynomial hypergraph constructions. We address the two major comments below and will incorporate clarifications in the revised manuscript.

read point-by-point responses

Referee: [Construction and quasi-randomness section (likely §3–4)] The load-bearing step is the proof that the multivariate polynomial hypergraphs simultaneously achieve constant edge density and sufficiently small discrepancy for the counting lemma to produce the claimed asymptotic. The manuscript must exhibit the precise character-sum or Fourier estimates establishing the discrepancy bound uniformly in the degree and field size; without these, the application to k-Diophantine m-tuples reduces to an unverified assumption.

Authors: Section 3 establishes constant edge density by direct counting and derives the discrepancy bound via character-sum estimates on the associated exponential sums over F_q. These estimates rely on the Weil bound and its higher-dimensional extensions and are stated to hold uniformly in the polynomial degree and in q. To address the concern, we will revise the section to display the precise character-sum bounds (including their explicit dependence on degree and q) immediately before the discrepancy statement, making the uniformity transparent. revision: yes
Referee: [Asymptotic counting argument (likely §5)] The asymptotic formula for the number of k-Diophantine m-tuples is stated to follow from the hypergraph counting argument, but the error term depends on the discrepancy; the paper should make explicit how the o(1) discrepancy translates into the error term in the final count, including dependence on m, k, and q.

Authors: The counting lemma in Section 5 produces an error bounded by a constant multiple of the discrepancy times a polynomial factor in q whose degree depends on m and k. Because the discrepancy tends to zero as q tends to infinity (uniformly for fixed m and k), the error is o(q^{appropriate power}). We will add an explicit paragraph in Section 5 tracing this dependence, stating the precise exponent of q in the error term and confirming that the o(1) statement holds for each fixed m and k. revision: yes

Circularity Check

0 steps flagged

No circularity; asymptotic formula derived from independent quasi-randomness of polynomial hypergraphs

full rationale

The derivation proceeds by constructing explicit families of hypergraphs from multivariate polynomials over finite fields, establishing their edge density and discrepancy bounds (via character-sum or Fourier estimates), and then applying a counting lemma to obtain the asymptotic count of k-Diophantine m-tuples. This answers an external question posed by Hammonds et al. No step reduces the count to a fitted parameter, self-definition, or load-bearing self-citation; the quasi-randomness properties are asserted as consequences of the polynomial construction and analytic estimates rather than being defined in terms of the Diophantine count itself. The paper is self-contained against external benchmarks and does not rename known results or smuggle ansatzes via prior self-work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, background axioms, or new entities; ledger is empty by necessity.

pith-pipeline@v0.9.0 · 5668 in / 1022 out tokens · 49303 ms · 2026-05-22T22:46:51.841507+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We define the k-uniform hypergraph Y_{f,q} on F_q such that a k-element subset forms an edge iff f(a1,...,ak) is a square; admissible polynomials satisfy non-square and primitive conditions; Theorem 1.3 proves N^*(Y_{f,q}, O_e^k) = q^{2k}/2 + O(q^{2k-1}) uniformly.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Corollary 1.6 gives the asymptotic q^m / (m! 2^{binom(m,k)}) + o(q^m) for k-Diophantine m-tuples via the Q1 property of the induced hypergraphs.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 1 internal anchor

[1]

Aigner-Horev and H

E. Aigner-Horev and H. e. H `an. Linear quasi-randomness of subsets of abelian groups and hypergraphs. European J. Combin., 88:103116, 16, 2020

work page 2020
[2]

G. o. Batta, L. Hajdu, and A. Pongr ´acz. On Diophantine graphs.J. Lond. Math. Soc. (2), 111(5):Paper No. e70163, 21, 2025

work page 2025
[3]

B ´erczes, A

A. B ´erczes, A. Dujella, L. Hajdu, and F. Luca. On the size of sets whose elements have perfect powern- shifted products.Publ. Math. Debrecen, 79(3-4):325–339, 2011

work page 2011
[4]

B ´erczes, A

A. B ´erczes, A. Dujella, L. Hajdu, and S. Tengely. Finiteness results forF-Diophantine sets.Monatsh. Math., 180(3):469–484, 2016

work page 2016
[5]

Bugeaud and K

Y . Bugeaud and K. Gyarmati. On generalizations of a problem of Diophantus.Illinois J. Math., 48(4):1105– 1115, 2004

work page 2004
[6]

Cafure and G

A. Cafure and G. Matera. Improved explicit estimates on the number of solutions of equations over a finite field.Finite Fields Appl., 12(2):155–185, 2006

work page 2006
[7]

F. R. K. Chung. Quasi-random classes of hypergraphs.Random Structures Algorithms, 1(4):363–382, 1990

work page 1990
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F. R. K. Chung and R. L. Graham. Quasi-random hypergraphs.Random Structures Algorithms, 1(1):105–124, 1990

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F. R. K. Chung, R. L. Graham, and R. M. Wilson. Quasi-random graphs.Combinatorica, 9(4):345–362, 1989

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Conlon, H

D. Conlon, H. H `an, Y . Person, and M. Schacht. Weak quasi-randomness for uniform hypergraphs.Random Structures Algorithms, 40(1):1–38, 2012

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Croot and C

E. Croot and C. H. Yip. Diophantine tuples and product sets in shifted powers, 2025. arXiv:2504.04354

work page arXiv 2025
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Dujella.Diophantinem-tuples and Elliptic Curves, volume 79 ofDevelopments in Mathematics

A. Dujella.Diophantinem-tuples and Elliptic Curves, volume 79 ofDevelopments in Mathematics. Springer, Cham, 2024

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Dujella and M

A. Dujella and M. Kazalicki. Diophantinem-tuples in finite fields and modular forms.Res. Number Theory, 7(1):Paper No. 3, 24, 2021

work page 2021
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A. M. G ¨ulo˘glu and M. R. Murty. The Paley graph conjecture and Diophantinem-tuples.J. Combin. Theory Ser. A, 170:105155, 9, 2020

work page 2020
[15]

Gyarmati

K. Gyarmati. On a problem of Diophantus.Acta Arith., 97(1):53–65, 2001

work page 2001
[16]

Gyarmati and A

K. Gyarmati and A. S ´ark¨ozy. Equations in finite fields with restricted solution sets. I. Character sums.Acta Math. Hungar., 118(1-2):129–148, 2008

work page 2008
[17]

Gyarmati, A

K. Gyarmati, A. S ´ark¨ozy, and C. L. Stewart. On shifted products which are powers.Mathematika, 49(1- 2):227–230, 2002

work page 2002
[18]

Hammonds, S

T. Hammonds, S. Kim, S. J. Miller, A. Nigam, K. Onghai, D. Saikia, and L. M. Sharma.k-Diophantine m-tuples in finite fields.Int. J. Number Theory, 19(4):891–912, 2023

work page 2023
[19]

Haviland and A

J. Haviland and A. Thomason. Pseudo-random hypergraphs. volume 75, pages 255–278. 1989. Graph theory and combinatorics (Cambridge, 1988)

work page 1989
[20]

B. He, A. Togb ´e, and V . Ziegler. There is no Diophantine quintuple.Trans. Amer. Math. Soc., 371(9):6665– 6709, 2019. 15

work page 2019
[21]

Kazalicki and B

M. Kazalicki and B. Naskrecki. Diophantine triples and K3 surfaces.J. Number Theory, 236:41–70, 2022

work page 2022
[22]

S. Kim, C. H. Yip, and S. Yoo. Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples. Canad. J. Math., to appear. arXiv:2309.09124

work page internal anchor Pith review Pith/arXiv arXiv
[23]

S. Kim, C. H. Yip, and S. Yoo. Paley-like quasi-random graphs arising from polynomials. arXiv:2405.09319, 2024

work page arXiv 2024
[24]

S. Kim, C. H. Yip, and S. Yoo. Explicit constructions of Diophantine tuples over finite fields.Ramanujan J., 65(1):163–172, 2024

work page 2024
[25]

Lang and A

S. Lang and A. Weil. Number of points of varieties in finite fields.Amer. J. Math., 76:819–827, 1954

work page 1954
[26]

Lidl and H

R. Lidl and H. Niederreiter.Finite fields, volume 20 ofEncyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, second edition, 1997

work page 1997
[27]

J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities.J. Assoc. Comput. Mach., 27(4):701–717, 1980

work page 1980
[28]

I. E. Shparlinski. On the number of Diophantinem-tuples in finite fields.Finite Fields Appl., 90:Paper No. 102241, 7, 2023

work page 2023
[29]

K. Slavov. Square values of several polynomials over a finite field.Finite Fields Appl., 109:Paper No. 102696, 2026

work page 2026
[30]

Thomason

A. Thomason. Pseudorandom graphs. InRandom graphs ’85 (Pozna ´n, 1985), volume 144 ofNorth-Holland Math. Stud., pages 307–331. North-Holland, Amsterdam, 1987

work page 1985
[31]

Thomason

A. Thomason. Random graphs, strongly regular graphs and pseudorandom graphs. InSurveys in combi- natorics 1987 (New Cross, 1987), volume 123 ofLondon Math. Soc. Lecture Note Ser., pages 173–195. Cambridge Univ. Press, Cambridge, 1987

work page 1987
[32]

C. H. Yip. Multiplicatively reducible subsets of shifted perfectkth powers and bipartite Diophantine tuples. Acta Arith., 218(3):251–271, 2025

work page 2025
[33]

C. H. Yip and S. Yoo.F-Diophantine sets over finite fields.Int. J. Number Theory, 21(5):1043–1050, 2025. DEPARTEMENTMATHEMATIK UNDINFORMATIK, UNIVERSIT ¨ATBASEL, SPIEGELGASSE1, 4051 BASEL, SWITZERLAND Email address:seoyoung.kim@unibas.ch SCHOOL OFMATHEMATICS, GEORGIAINSTITUTE OFTECHNOLOGY, ATLANTA, GA 30332, UNITED STATES Email address:cyip30@gatech.edu D...

work page 2025

[1] [1]

Aigner-Horev and H

E. Aigner-Horev and H. e. H `an. Linear quasi-randomness of subsets of abelian groups and hypergraphs. European J. Combin., 88:103116, 16, 2020

work page 2020

[2] [2]

G. o. Batta, L. Hajdu, and A. Pongr ´acz. On Diophantine graphs.J. Lond. Math. Soc. (2), 111(5):Paper No. e70163, 21, 2025

work page 2025

[3] [3]

B ´erczes, A

A. B ´erczes, A. Dujella, L. Hajdu, and F. Luca. On the size of sets whose elements have perfect powern- shifted products.Publ. Math. Debrecen, 79(3-4):325–339, 2011

work page 2011

[4] [4]

B ´erczes, A

A. B ´erczes, A. Dujella, L. Hajdu, and S. Tengely. Finiteness results forF-Diophantine sets.Monatsh. Math., 180(3):469–484, 2016

work page 2016

[5] [5]

Bugeaud and K

Y . Bugeaud and K. Gyarmati. On generalizations of a problem of Diophantus.Illinois J. Math., 48(4):1105– 1115, 2004

work page 2004

[6] [6]

Cafure and G

A. Cafure and G. Matera. Improved explicit estimates on the number of solutions of equations over a finite field.Finite Fields Appl., 12(2):155–185, 2006

work page 2006

[7] [7]

F. R. K. Chung. Quasi-random classes of hypergraphs.Random Structures Algorithms, 1(4):363–382, 1990

work page 1990

[8] [8]

F. R. K. Chung and R. L. Graham. Quasi-random hypergraphs.Random Structures Algorithms, 1(1):105–124, 1990

work page 1990

[9] [9]

F. R. K. Chung, R. L. Graham, and R. M. Wilson. Quasi-random graphs.Combinatorica, 9(4):345–362, 1989

work page 1989

[10] [10]

Conlon, H

D. Conlon, H. H `an, Y . Person, and M. Schacht. Weak quasi-randomness for uniform hypergraphs.Random Structures Algorithms, 40(1):1–38, 2012

work page 2012

[11] [11]

Croot and C

E. Croot and C. H. Yip. Diophantine tuples and product sets in shifted powers, 2025. arXiv:2504.04354

work page arXiv 2025

[12] [12]

Dujella.Diophantinem-tuples and Elliptic Curves, volume 79 ofDevelopments in Mathematics

A. Dujella.Diophantinem-tuples and Elliptic Curves, volume 79 ofDevelopments in Mathematics. Springer, Cham, 2024

work page 2024

[13] [13]

Dujella and M

A. Dujella and M. Kazalicki. Diophantinem-tuples in finite fields and modular forms.Res. Number Theory, 7(1):Paper No. 3, 24, 2021

work page 2021

[14] [14]

A. M. G ¨ulo˘glu and M. R. Murty. The Paley graph conjecture and Diophantinem-tuples.J. Combin. Theory Ser. A, 170:105155, 9, 2020

work page 2020

[15] [15]

Gyarmati

K. Gyarmati. On a problem of Diophantus.Acta Arith., 97(1):53–65, 2001

work page 2001

[16] [16]

Gyarmati and A

K. Gyarmati and A. S ´ark¨ozy. Equations in finite fields with restricted solution sets. I. Character sums.Acta Math. Hungar., 118(1-2):129–148, 2008

work page 2008

[17] [17]

Gyarmati, A

K. Gyarmati, A. S ´ark¨ozy, and C. L. Stewart. On shifted products which are powers.Mathematika, 49(1- 2):227–230, 2002

work page 2002

[18] [18]

Hammonds, S

T. Hammonds, S. Kim, S. J. Miller, A. Nigam, K. Onghai, D. Saikia, and L. M. Sharma.k-Diophantine m-tuples in finite fields.Int. J. Number Theory, 19(4):891–912, 2023

work page 2023

[19] [19]

Haviland and A

J. Haviland and A. Thomason. Pseudo-random hypergraphs. volume 75, pages 255–278. 1989. Graph theory and combinatorics (Cambridge, 1988)

work page 1989

[20] [20]

B. He, A. Togb ´e, and V . Ziegler. There is no Diophantine quintuple.Trans. Amer. Math. Soc., 371(9):6665– 6709, 2019. 15

work page 2019

[21] [21]

Kazalicki and B

M. Kazalicki and B. Naskrecki. Diophantine triples and K3 surfaces.J. Number Theory, 236:41–70, 2022

work page 2022

[22] [22]

S. Kim, C. H. Yip, and S. Yoo. Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples. Canad. J. Math., to appear. arXiv:2309.09124

work page internal anchor Pith review Pith/arXiv arXiv

[23] [23]

S. Kim, C. H. Yip, and S. Yoo. Paley-like quasi-random graphs arising from polynomials. arXiv:2405.09319, 2024

work page arXiv 2024

[24] [24]

S. Kim, C. H. Yip, and S. Yoo. Explicit constructions of Diophantine tuples over finite fields.Ramanujan J., 65(1):163–172, 2024

work page 2024

[25] [25]

Lang and A

S. Lang and A. Weil. Number of points of varieties in finite fields.Amer. J. Math., 76:819–827, 1954

work page 1954

[26] [26]

Lidl and H

R. Lidl and H. Niederreiter.Finite fields, volume 20 ofEncyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, second edition, 1997

work page 1997

[27] [27]

J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities.J. Assoc. Comput. Mach., 27(4):701–717, 1980

work page 1980

[28] [28]

I. E. Shparlinski. On the number of Diophantinem-tuples in finite fields.Finite Fields Appl., 90:Paper No. 102241, 7, 2023

work page 2023

[29] [29]

K. Slavov. Square values of several polynomials over a finite field.Finite Fields Appl., 109:Paper No. 102696, 2026

work page 2026

[30] [30]

Thomason

A. Thomason. Pseudorandom graphs. InRandom graphs ’85 (Pozna ´n, 1985), volume 144 ofNorth-Holland Math. Stud., pages 307–331. North-Holland, Amsterdam, 1987

work page 1985

[31] [31]

Thomason

A. Thomason. Random graphs, strongly regular graphs and pseudorandom graphs. InSurveys in combi- natorics 1987 (New Cross, 1987), volume 123 ofLondon Math. Soc. Lecture Note Ser., pages 173–195. Cambridge Univ. Press, Cambridge, 1987

work page 1987

[32] [32]

C. H. Yip. Multiplicatively reducible subsets of shifted perfectkth powers and bipartite Diophantine tuples. Acta Arith., 218(3):251–271, 2025

work page 2025

[33] [33]

C. H. Yip and S. Yoo.F-Diophantine sets over finite fields.Int. J. Number Theory, 21(5):1043–1050, 2025. DEPARTEMENTMATHEMATIK UNDINFORMATIK, UNIVERSIT ¨ATBASEL, SPIEGELGASSE1, 4051 BASEL, SWITZERLAND Email address:seoyoung.kim@unibas.ch SCHOOL OFMATHEMATICS, GEORGIAINSTITUTE OFTECHNOLOGY, ATLANTA, GA 30332, UNITED STATES Email address:cyip30@gatech.edu D...

work page 2025