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%I #28 Jan 24 2019 16:48:11
%S 2165017,15512114571284835412957,
%T 368440923990671763222767414151367493861848396861,
%U 29032470413228645503712143213832535500985227130245791625262982715784415755764157625
%N Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.
%C Square roots of the hypotenuses of Pythagorean triangles in which the hypotenuse and the sum of the legs are squares. In a letter to Mersenne in the year 1643, Fermat asserted that the smallest such triangle has the legs 456548602761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.
%C Subsequence of A166929 which allows a,b be nonzero.
%C Values of m in coprime solutions to 2m^4 = c^4 + d^2 with d < c^2 (so that a,b = (c^2 +- d)/2). Corresponding values of c are given in A167438.
%C Terms 5..8 found. - _Gerry Martens_, Jan 15 2019
%D W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.
%H Gerry Martens, <a href="/A166930/b166930.txt">Table of n, a(n) for n = 1..13</a>
%Y Cf. A166929, A167437, A167438.
%K nonn
%O 1,1
%A _Max Alekseyev_, Oct 23 2009
%E Edited by _Max Alekseyev_, Nov 03 2009
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