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Composite n such that binomial(5*n,n) == 5^n (mod n).
2

%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