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A061408
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For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both positive squares; list all such pairs (x,y) ordered by values of y; sequence gives y values.
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5
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4, 6, 8, 10, 12, 12, 14, 16, 16, 18, 20, 20, 22, 24, 24, 24, 26, 28, 28, 30, 30, 32, 32, 34, 36, 36, 36, 38, 40, 40, 40, 42, 42, 44, 44, 46, 48, 48, 48, 48, 50, 52, 52, 54, 54, 56, 56, 56, 58, 60, 60, 60, 60, 62, 64, 64, 64, 66, 66, 68, 68, 70, 70, 72
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OFFSET
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0,1
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COMMENTS
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REFERENCES
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Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.
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LINKS
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FORMULA
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The solutions are given by x = r^2 + 2*r*k + 2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1. - N. J. A. Sloane, May 02 2001
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EXAMPLE
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Pairs are [5, 4], [10, 6], [17, 8], [26, 10], [13, 12], [37, 12], [50, 14], ... For example, 5-4 = 1^2, 5+4 = 3^2.
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MAPLE
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seq(y $ nops(select(t -> (t^2 < y/2), numtheory:-divisors(y/2))), y=2..100, 2); # Robert Israel, Dec 10 2017
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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