All Questions

Do there exist positive integers $a,b$ and a prime $p>\max(a,b)$ such that $p^3$ divides $(a+b)^p-a^p-b^p$? The reader of Kvant magazine A. T. Kurgansky asked to prove that such $a,b,p$ do not ...

From the literature, showed below, I know two gadgets that provide a way to know if a positive integer (a positive quantity of units) is composite or a prime number. I would like to know if in the ...

We are trying to show that primes of the form $a(n)$ can't be Wieferich primes. For natural $n$ define $J(n)=(2^{n-1}-1) \bmod n^2$ and if $n$ is power of two define $J(2^n)=1$ (this is artificial, ...