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%I #14 Sep 08 2022 08:45:58
%S 5,0,0,3,4,0,0,0,3,0,2,0,0,0,0,5,0,0,2,0,0,0,0,0,1,0,0,0,4,0,4,0,0,0,
%T 0,1,0,0,0,0,4,0,0,4,0,0,0,0,1,0,0,0,0,0,6,0,0,0,2,0,4,0,0,3,0,0,0,0,
%U 0,0,4,0,0,0,0,0,0,0,2,4,5,0,0,0,0,0
%N a(n)=Number of integer solutions of quartic elliptic curve y^2 = 5x^4 + 4n.
%C Quintic trinomial x^5-nx+m is reducible into cubic and quadratic factors if and only a(n)<>0.
%C Particular case for n=1 x^5-x+m have 3 solutions for m<>0 see A179106. Rest two (5-3) giving m=0.
%o (Magma) [IntegralQuarticPoints([5,0,0,0,4*n]) : n in [1..50]];
%K nonn
%O 1,1
%A _Artur Jasinski_, Jul 29 2011
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