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By exploiting the relation between $g(k,q)$ with the diameter of the generalized Paley graph $\\Gamma(k,q)$ and by using the characterization due to Pearce and Praeger (2019) of those $\\Gamma(k,q)$ which are Cartesian decomposable, we obtain the reduction formula\n  $$g(\\tfrac{p^{ab}-1}{bc},p^{ab}) = b g(\\tfrac{p^a-1}{c},p^a)$$ for $p$ prime and $a,b,c$ positive integers under certain arithmetic conditions. Then, we find some arithmetic conditions to apply the formula above, which allow us to obtain ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1911.12761","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-28T15:59:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5b630d479460ff72d519e0688a8ff70ad199435f874b9e57181cc4e569953a2e","abstract_canon_sha256":"0e46ef37c38021be08f35ff19aa23cf26349c6da8e829bd8a7d0f29b3349f04a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:29:06.556395Z","signature_b64":"c/2Jc0aQB/Zk4vMk1ovMaHZ/2bUeeHaLSKbgv8lYWdY7e539OXDK6JMr1KR3PStOSa4co8B/Jl401kUjPd9yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf0bc2d6a62d8fc12315a0bf378f3c610295e66da7fa94727f83d5563449cfe","last_reissued_at":"2026-07-05T04:29:06.555980Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:29:06.555980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A reduction formula for Waring numbers through generalized Paley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Denis E. Videla, Ricardo A. Podest\\'a","submitted_at":"2019-11-28T15:59:11Z","abstract_excerpt":"We give a reduction formula for the Waring number $g(k,q)$ over a finite field $\\mathbb{F}_q$. By exploiting the relation between $g(k,q)$ with the diameter of the generalized Paley graph $\\Gamma(k,q)$ and by using the characterization due to Pearce and Praeger (2019) of those $\\Gamma(k,q)$ which are Cartesian decomposable, we obtain the reduction formula\n  $$g(\\tfrac{p^{ab}-1}{bc},p^{ab}) = b g(\\tfrac{p^a-1}{c},p^a)$$ for $p$ prime and $a,b,c$ positive integers under certain arithmetic conditions. 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