[seqfan] Difficult to disprove
Tomasz Ordowski
tomaszordowski at gmail.com
Sun Apr 29 08:37:09 CEST 2018
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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