Search: id:A075760
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%I A075760
%S A075760 36,1225,19600,41616,1413721,48024900,1631432881,55420693056,
%T A075760 1882672131025
%N A075760 Nontrivial binomial coefficients which are perfect powers (A001597).
%C A075760 Triangular-square numbers (A001110) are a subset, except for 0 and 1.
%C A075760 "For C(n,k) k>=4 and any l>=2 no solutions exist and this is what Erdos 
               proved by an ingenious argument. ... C(50, 3) = 140^2 is the only 
               solution for k = 3, l=2." page 13 of Aigner and Ziegler.
%D A075760 Martin Aigner and Gunter M. Ziegler, Proofs from THE BOOK, Second Edition, 
               Springer-Verlag, Berlin, 2000, Chapter 3, "Binomial coefficients 
               are (almost) never powers," pages 13-16.
%t A075760 f[n_] := Apply[ GCD, Last[ Transpose[ FactorInteger[n]]]]; a = {}; Do[ 
               If[ f[n(n - 1)/2] > 1, a = Append[a, Binomial[n, 2]]]; If[ f[n(n 
               - 1)*(n - 2)/6] > 1, a = Append[a, Binomial[n, 3]]], {n, 5, 1500000}]
%Y A075760 Cf. A001110.
%Y A075760 Sequence in context: A151584 A103278 A004294 this_sequence A113938 A001110 
               A064196
%Y A075760 Adjacent sequences: A075757 A075758 A075759 this_sequence A075761 A075762 
               A075763
%K A075760 nonn
%O A075760 1,1
%A A075760 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 08 2002

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