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A166929 Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some coprime integers a, b, c. 3
1, 13, 1525, 2165017, 42422452969, 7658246457672229, 15512114571284835412957, 452005526897888844293504165425, 126314830357375266295717376544111167953, 368440923990671763222767414151367493861848396861 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Values of m in coprime solutions to 2m^4 = c^4 + d^2 (so that a, b = (c^2 +- d)/2).

Corresponding values of c are given in A167437.

Terms with positive a,b,c are given in A166930.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a/m^2 = (-8*u^2 + 32*v + u^4 + 4*v^2 - 4*u^3 + 16*u*v)/(8 + u^2 + 4*u)^2 and b/m^2 = (4*u^3 - 8*u^2 - 4*v*u^2 - 16*u*v + 64)/(8 + u^2 + 4*u)^2 where (u,v) is a rational point on the elliptic curve v^2 = u^3 + 8*u.

CROSSREFS

Sequence in context: A185193 A066457 A203515 * A079917 A028450 A201177

Adjacent sequences:  A166926 A166927 A166928 * A166930 A166931 A166932

KEYWORD

nonn

AUTHOR

Max Alekseyev, Oct 23 2009

EXTENSIONS

Edited by Max Alekseyev, Nov 03 2009

STATUS

approved

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Last modified July 7 23:03 EDT 2020. Contains 335502 sequences. (Running on oeis4.)