All Questions

Let $M_n$ denote the Mersenne numbers $M_n=2^n-1$. As $n$ varies, must $M_n$ be divisible by arbitrary large prime $p$ with exponent one, i.e. $p \mid M_n, p^2 \nmid M_n$? In other words, must the ...

We got argument and strong experimental support that integers of the form $n=p q^2$ can be factored using elliptic curves easier than general integers Q1 Is this known? Added This is known since at ...