[seqfan] Difficult to disprove

[Tomasz Ordowski]

Dear SeqFan,

I have a new conjecture:

There are no Carmichael numbers of the form (b^k-1)/(b-1),
where k is a Carmichael number and gcd(k,b-1)=1.

Note: Also valid for negative bases b.

Is there a chance to find a counterexample?

Best regards,

Thomas
________________________
Steuerwald's theorem (1948): If n is a weak psp(b) and gcd(n,b-1)=1, then
(b^n-1)/(b-1) is a psp(b).

Note that every Carmichael number k is weak psp(b) to all integer bases b.

And yet I put forward such a bold conjecture. Very difficult to disprove!




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