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%I #7 Jul 23 2014 12:06:11
%S 18,25,133,2107,4676,226037,4477739,827867201
%N Composite n such that binomial(7*n, n) == 7^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 18 is a term because binomial(7*18, 18) = 2797093093529137508875, 7^18 = 1628413597910449 and 2797093093529137508875 mod 18 = 1628413597910449 mod 18 = 1.
%t Do[If[ !PrimeQ[n], If[Mod[Binomial[7*n, n], n] == Mod[7^n, n], Print[n]]], {n, 2, 20000}]
%Y Cf. A080469.
%K more,nonn
%O 1,1
%A _Ryan Propper_, Aug 13 2005
%E 226037 from _Max Alekseyev_, Sep 13 2009
%E Two more terms from _Max Alekseyev_, Nov 06 2009
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