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      On a congruence conjecture of Z.-W. Sun involving Franel numbers

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          Abstract

          In this paper, we mainly prove the following conjecture of Z.-W. Sun \cite{S13}: Let p>2 be a prime. If p=x2+3y2 with x,yZ and x1(mod3), then x14p1k=0(3k+4)fk2k12p1k=0(3k+2)fk(4)k(modp2),

          where fn=nk=0(nk)3 stands for the nth Franel number.

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          Author and article information

          Journal
          16 November 2021
          Article
          2111.08775
          65ac39f5-7a0d-4936-bc28-607636ecbd02

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          10pages
          math.NT math.CO

          Combinatorics,Number theory
          Combinatorics, Number theory

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