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A166930
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Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.
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3
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2165017, 15512114571284835412957, 368440923990671763222767414151367493861848396861, 29032470413228645503712143213832535500985227130245791625262982715784415755764157625
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OFFSET
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1,1
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COMMENTS
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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.
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.
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REFERENCES
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W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.
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LINKS
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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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