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 ...

Given an $m$ by $n$ matrix $A$ I'm familiar with the standard method to compute a basis for the null space of $A$ by computing a QR factorization of $A^T$. If $A$ is large and sparse, we can use ...

I have two questions about the class of integer-coefficient polynomials all of whose roots are rational. I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!) ...

Although I am also interested in the number of distinct prime factors (not counting multiplicity), today I use $\omega(m)$ to denote the number of (positive) prime factors (with multiplicity) of the ...

In Proposition 1.1 of [Math. Proc. Cambridge Phil. Soc. 64 (1968), No. 2, 251-264], P.M. Cohn famously claimed (without proof) that a commutative domain is atomic if and only if it satisfies the ...