[seqfan] A015919
Tomasz Ordowski
tomaszordowski at gmail.com
Mon Apr 16 13:10:32 CEST 2018
Hello, see
http://oeis.org/A015919
Theorem: if n is a term, then so is 2^n-1.
Conjecture: if 2^n-1 is a term, then so is n.
How far can you check my conjecture?
Please reply.
Best regards,
Thomas
P.S. Generally:
Let B be the set of natural numbers n such that
(b^n-1)/(b-1) == 1 (mod n)
with a fixed integer b > 1.
My Last Conjecture:
The number (b^k-1)/(b-1) belongs to the set B if and only if k belongs to
B.
Note: This can be extended to bases b < -1.
________________________
Steuerwald's theorem (1948): If k is a psp(b) and gcd(k,b-1)=1, then
(b^k-1)/(b-1) is a psp(b).
Here a composite k is a psp(b) if and only if b^k == b (mod k).
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