Generalizations of Carmichael numbers I

Romeo Meštrović

A composite positive integer $n$ is said to be a {\it weak Carmichael number} if $$ \sum_{\gcd(k,n)=1\atop 1\le k\le n-1}k^{n-1}\equiv φ(n) \pmod{n}. \leqno(1) $$ It is proved that…