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%I #7 Jul 23 2014 12:05:47
%S 4,365,400,685,3200,6400,12550,12800,16525,25600,51200,225125,
%T 70463125,271094125,431434441
%N Composite n such that binomial(5*n,n) == 5^n (mod n).
%C No other terms below 10^9.
%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for various problems</a>
%e 4 is a term because binomial(5*4, 4) = 4845, 5^4 = 625 and 4845 mod 4 = 625 mod 4 = 1.
%t Do[If[ !PrimeQ[n], If[Mod[Binomial[5*n, n], n] == Mod[5^n, n], Print[n]]], {n, 1, 50000}]
%Y Cf. A080469.
%K hard,more,nonn
%O 1,1
%A _Ryan Propper_, Aug 12 2005
%E a(12) from _D. S. McNeil_, Mar 15 2009
%E 225125 from _Max Alekseyev_, Sep 13 2009
%E Three more terms from _Max Alekseyev_, Nov 06 2009
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