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Smallest k such that k^2+1 is divisible by A002144(n)^9.
2

%I #3 Mar 30 2012 17:27:56

%S 280182,822557039,24306922095,4563230639355,15069267560119,

%T 112076323050317,50928660480181,3138611770750343,9110883894036198,

%U 50251663587824641,76004727767164666,310872228812491206,521749964271465

%N Smallest k such that k^2+1 is divisible by A002144(n)^9.

%e a(1) = 280182 since A002144(1) = 5, 280182^2+1 = 78501953125 = 5^9*40193 and for no k < 280182 does 5^9 divide k^2+1. a(3) = 24306922095 since A002144(3) = 17, 24306922095^2+1 = 590826461732399189026 = 2*17^9*29*673*127637 and for no k < 24306922095 does 17^9 divide k^2+1.

%Y Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298, A145299, A145871, A145872.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Oct 30 2008