On generalised Carmichael numbers.
On generalised Carmichael numbers.
For arbitrary integers $k\in\mathbb Z$, we investigate the set $C_k$ of the generalised Carmichael number, i.e. the natural numbers $n< \max\{1, 1-k\}$ such that the equation $a^{n+k}\equiv a \mod n$ holds for all $a\in\mathbb N$. We give a characterization of these generalised Carmichael numbers and discuss several special cases. In …