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Proof of a conjectural supercongruence modulo p⁵
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Proof of a conjectural supercongruence modulo p⁵
classification
math.NT
keywords
fracsupercongruencebinomconjecturalconjecturedequivmodulopmod
read the original abstract
In this paper we prove the supercongruence $$\sum_{n=0}^{(p-1)/2}\frac{6n+1}{256^n}\binom{2n}n^3\equiv p(-1)^{(p-1)/2}+(-1)^{(p-1)/2}\frac{7}{24}p^4B_{p-3}\pmod{p^5}$$ for any prime $p>3$, which was conjectured by Sun in 2019.
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