Proves that for primes p ≡ 3 mod 4, twice a specific determinant involving Legendre symbols is a quadratic residue mod p, and that the permanent of a power matrix [j^{k-1}] is divisible by n when n > 1 and n ≢ 2 mod 4.
Sun,Problems and results on determinants involving Legendre symbols, Bull
2 Pith papers cite this work. Polarity classification is still indexing.
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math.NT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves explicit determinant formulas and a uniform congruence modulo p for Legendre symbol matrices, resolving parts of Sun's conjectures 4.8(i) and 4.10(i).
citing papers explorer
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Some new results on determinants and permanents
Proves that for primes p ≡ 3 mod 4, twice a specific determinant involving Legendre symbols is a quadratic residue mod p, and that the permanent of a power matrix [j^{k-1}] is divisible by n when n > 1 and n ≢ 2 mod 4.
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Two determinant evaluations in Sun's conjectures involving Legendre symbols
Proves explicit determinant formulas and a uniform congruence modulo p for Legendre symbol matrices, resolving parts of Sun's conjectures 4.8(i) and 4.10(i).