$(a,a)$-Carmichael numbers and greatest common divisors of $p-a$

Thomas Wright

Define an $(a,a)$-Carmichael number to be a squarefree natural number $n$ such that $p\mid n$ implies $p-a\mid n-a$. For such a number $n$ with prime factors $p_1,\cdots ,p_m$, defi…