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A229848 Values of n such that the equation x^2 - 3*n*y^2 = n has integer solutions. 1

%I

%S 1,4,7,9,13,16,19,25,28,31,36,37,43,49,52,61,63,64,67,76,79,81,91,100,

%T 103,109,112,117,121,124,127,139,144,148,151,157,163,169,171,172,175,

%U 181,193,196,199,208,211,217,223,225,229,244,247,252,256,268,271

%N Values of n such that the equation x^2 - 3*n*y^2 = n has integer solutions.

%e 37 appears in the sequence because the equation x^2 - 111*y^2 = 37 has integer solutions.

%t Select[Range[300],Length[FullSimplify[Solve[x^2-3*#*y^2==#,{x,y},Integers]/.C[1]->1]]>0&] (* _Vaclav Kotesovec_, Oct 08 2013 *)

%Y Cf. A172000, A227939

%K nonn

%O 1,2

%A _Colin Barker_, Oct 07 2013

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)