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Super Carmichael numbers are Carmichael numbers

A super Carmichael number is a weak Carmichael number satisfying

∑1≤k≤n−1gcd⁡(k,n)=1kn−1≡φ(n)(modn2).\sum_{\substack{1\le k\le n-1\gcd(k,n)=1}}k^{n-1}\equiv\varphi(n)\pmod{n^2}.

Super-Carmichael containment conjecture. Every super Carmichael number is a Carmichael number. The source presents this as a heuristic conjecture based on computations and the expectation that super Carmichael numbers occur only among Carmichael numbers.

Sources & referencesView supporting material

Primary source

Romeo Meštrović, “Generalizations of Carmichael numbers I”, arXiv:1305.1867 (2013).

carmichael-numbersweak-carmichael-numbers

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