Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.4

A New Solution to the Equation τ(p) ≡ 0 (mod p)

Nik Lygeros
14 av. Condorcet
69100 Villeurbanne

Olivier Rozier
113 av. de la Dhuys
93170 Bagnolet


The known solutions to the equation τ(p) ≡ 0 (mod p) were p = 2, 3, 5, 7, and 2411. Here we present our method to compute the next solution, which is p = 7758337633. There are no other solutions up to 1010.

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(Concerned with sequences A000108 A000245 A000344 A000594 A002057 A003517 A007659 A008315 A009766 A058305 A058306 A108786.)

Received May 7 2010; revised version received June 30 2010. Published in Journal of Integer Sequences, July 9 2010.

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