[seqfan] About squarefree numbers (2^n-1)/gcd(n, 2^n-1) and (2^n+1)/gcd(n, 2^n+1)
tomaszordowski at gmail.com
Sat Dec 8 14:36:58 CET 2018
I formulated the following theorems (easy to prove):
The smallest numerator of (2^n-1) / n is not squarefree
if and only if n = k ord_q(2) for k = 1, 2, 3, ...;
where q is a Wieferich prime (1093 and 3511).
The smallest numerator of (2^n+1) / n is not squarefree
if and only if n = (2k+1) ord_q(2) / 2 for k = 0, 1, 2, ...;
where q is a Wieferich prime (1093).
Are these well-known facts?
ord_1093(2) = 364,
ord_3511(2) = 1755;
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