A166930 - OEIS

A166930

Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.

%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