A178900 - OEIS

A178900

First nonzero value of (a^(p-1) - 1) mod p^2, for a > 0 coprime to the n-th Wieferich prime p.

341016, 24577

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OFFSET

1,1

COMMENTS

It is believed that a(n) = (3^(p-1) - 1) mod p^2 for all n, where p = A001220(n).

See additional comments, references, links and cross-references in A001220.

LINKS

A. Ostafe and I. Shparlinski (2010), Pseudorandomness and Dynamics of Fermat Quotients, arXiv:1001.1504 [math.NT], 2010.

FORMULA

a(n) = (A178815(A000720(p))^(p-1) - 1) mod p^2, where p = A001220(n).

a(n) mod p = A178844(A000720(p)), where p = A001220(n).

EXAMPLE

The first Wieferich prime is 1093 and a^1092 - 1 mod 1093^2 = 0, 0, 341016 for a = 1, 2, 3, so a(1) = 341016.

CROSSREFS

KEYWORD

bref,hard,more,nonn

AUTHOR

STATUS

approved