[seqfan] A strong question
Tomasz Ordowski
tomaszordowski at gmail.com
Sun Nov 25 18:57:36 CET 2018
Dear SeqFans!
Let's define:
Composite numbers m such that b^(m-1) == 1 (mod (b^2-1)m) has a solution b.
25, 49, 65, 85, 91, 121, 125, 133, 145, 169, 185, 205, 217, 221, 247, 259,
...
Note: If such m exists, then the smallest b is in the range 2 <= b <= m-2.
Conjecture:
If m is a composite number such that b^(m-1) == 1 (mod (b^2-1)m) for some
b,
then m is a strong pseudoprime to some base a in the range 2 <= a <= m-2.
Note that not always the smallest a = b.
The question: Is this a proper subset of A181782 ?
Are my pseudoprimes stronger than the strong pseudoprimes?
Cf. https://oeis.org/A181782 (strong pseudoprimes to some base).
Best regards,
Thomas Ordowski
P.S. Let a(n) be the smallest composite k such that n^(k-1) == 1 (mod
(n^2-1)k), for n > 1.
341, 91, 91, 217, 481, 25, 65, 91, 91, 133, 133, 85, 781, 341, 91, 91, 25,
49, 671, 221, 169, ...
The sequence is not in OEIS.
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