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Infinitely many super Carmichael numbers

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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 infinitude conjecture. There are infinitely many super Carmichael numbers. The source motivates this by heuristic estimates based on the abundance of Carmichael numbers.

References

Primary source

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

carmichael-numbersprime-distribution
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