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 A060829 For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both squares; list all such pairs (x,y) with gcd(x,y) = 1 ordered by values of y; sequence gives x values. 4

%I

%S 5,17,13,37,65,29,101,25,145,53,197,257,85,325,41,401,125,485,73,577,

%T 173,677,65,785,61,109,229,901,1025,293,1157,97,1297,365,1445,89,1601,

%U 85,205,445,137,533,265,629,185,733,113,845,169,241,409

%N For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both squares; list all such pairs (x,y) with gcd(x,y) = 1 ordered by values of y; sequence gives x values.

%D Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.

%F The solutions are given by x = r^2+2*r*k+2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1, r odd, gcd(r, k) = 1.

%e Pairs are [5, 4], [17, 8], [13, 12], [37, 12], [65, 16], [29, 20], [101, 20], ... E.g. 5-4=1^2, 5+4=3^2.

%Y Cf. A060830, A061408, A061409.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, May 02 2001

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