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A125610 Smallest prime p such that 5^n divides p^4 - 1.

%I A125610 #17 Mar 20 2025 22:34:05
%S A125610 2,7,193,443,14557,14557,735443,3124999,7812499,78124999,292968749,
%T A125610 853235443,2441406251,53834264557,122070312499,202513391693,
%U A125610 1118040735443,3459595983307,3459595983307,270488404577057
%N A125610 Smallest prime p such that 5^n divides p^4 - 1.
%H A125610 Robert Israel, <a href="/A125610/b125610.txt">Table of n, a(n) for n = 1..1424</a>
%H A125610 W. Keller and J. Richstein <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>.
%p A125610 f:= proc(n) local k, p2,P,t;
%p A125610     p2:= numtheory:-msqrt(-1,5^n);
%p A125610     P:= sort([1,p2,5^n-p2,5^n-1]);
%p A125610     for k from 0 do
%p A125610       for t in P do
%p A125610         if isprime(k*5^n+t) then return k*5^n+t fi
%p A125610     od od:
%p A125610 end proc:
%p A125610 map(f, [$1..30]); # _Robert Israel_, Oct 27 2019
%o A125610 (PARI) \\ See A125609 - _Martin Fuller_, Jan 11 2007
%Y A125610 Cf. A125609 = Smallest prime p such that 3^n divides p^2 - 1. Cf. A125611 = Smallest prime p such that 7^n divides p^6 - 1. Cf. A125612 = Smallest prime p such that 11^n divides p^10 - 1. Cf. A125632 = Smallest prime p such that 13^n divides p^12 - 1. Cf. A125633 = Smallest prime p such that 17^n divides p^16 - 1. Cf. A125634 = Smallest prime p such that 19^n divides p^18 - 1. Cf. A125635 = Smallest prime p such that 257^n divides p^256 - 1.
%K A125610 hard,nonn
%O A125610 1,1
%A A125610 _Alexander Adamchuk_, Nov 28 2006
%E A125610 More terms from _Ryan Propper_, Jan 02 2007
%E A125610 More terms from _Martin Fuller_, Jan 11 2007