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

Offset: 1

Author

Jonathan Sondow, Jun 23 2010

Keywords

• bref
• hard
• more
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001220, A178815, A178844.

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).