Proof of a supercongruence conjectured by Sun through a q-microscope

2019/12/15 by Guo, Victor J. W.
#11A07 #11B65 #33D15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.08070

Abstract

Recently, Z.-W. Sun made the following conjecture: for any odd prime p and odd integer m, \frac1m²m-1\choose (m-1)/2(∑_k=0^(pm-1)/2(2k\choose k)/(8^k) -((2)/(p))∑_k=0^(m-1)/2(2k\choose k)/(8^k)) ≡ 0\pmodp². In this note, applying the "creative microscoping" method, introduced by the author and Zudilin, we confirm the above conjecture of Sun.

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