[seqfan] Theorem

[Tomasz Ordowski]

Dear SeqFans,

I have an interesting theorem, namely:

If p > 3 is a prime, then b^{m/(b-1)-1} == 1 (mod m^2+m+1), where m =
b^p-1.

It works for bases b = 2, 3, 5. How to generalize this theorem to other
bases?

What composite numbers p for a given base b are pseudoprimes here?

MERRY CHRISTMAS AND HAPPY NEW YEAR !

Thomas
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https://oeis.org/draft/A066488