[seqfan] 5, 91, 4369, 406901, ...

[Tomasz Ordowski]

Dear readers,

I noticed something interesting.

Let a(n) = (n^(2n)-1)/(n^2-1) for n > 1.
For example a(10) = 1010101010101010101.
Conjecture: for n > 2, a(n) is a pseudoprime to base n.
For an odd prime p, a(p) is a Cipolla pseudoprime to base p.
Is a(m) a Fermat pseudoprime to base m for every composite m ?
Amiram Eldar confirmed this up to m = 3800.
Find formal proof.

Best regards,

Thomas Ordowski
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