3 problems

Let $B_m$ denote the $m$th Bernoulli number, written in lowest terms when referring to its numerator. Bernoulli nondivisibility conjecture. There are infinitely many primes $p$ suc…

Let $S_m(n)=\sum_{j=1}^{n-1}j^m$. Fourth-power Wolstenholme congruence conjecture. For no integer $n\ge 2$ does the congruence … hold. The source presents this as a computationally…

Let $p$ be a prime, and let … or … A Wolstenholme prime is a prime satisfying ${2p-1\choose p-1}\equiv1\pmod{p^4}$. Meštrović's conjecture. Either of the preceding congruences for…