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.

2165017, 15512114571284835412957, 368440923990671763222767414151367493861848396861, 29032470413228645503712143213832535500985227130245791625262982715784415755764157625

Offset

1,1

Comments

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 4565486027761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.

Subsequence of A166929 which allows a,b be nonzero.

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.

References

W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.

J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, pp. 413-419.

Links

Gerry Martens, Table of n, a(n) for n = 1..13

Crossrefs

Cf. A166929, A167437, A167438.

Sequence in context: A253762 A154874 A258421 * A183754 A049359 A105711

Adjacent sequences: A166927 A166928 A166929 * A166931 A166932 A166933

Keyword

nonn,changed

Author

Max Alekseyev, Oct 23 2009

Extensions

Edited by Max Alekseyev, Nov 03 2009

Status

approved