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A268603
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Denominator of the side lengths (legs in ascending order) of the easiest Pythagorean Triangle (with smallest hypotenuse) according to the congruent numbers A003273.
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1
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2, 3, 6, 1, 1, 1, 12, 5, 60, 323, 30, 9690, 3, 2, 6, 1, 2, 2, 1, 3, 3, 2, 1, 2, 35, 3, 105, 20748, 3485, 72306780
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OFFSET
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1,1
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COMMENTS
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Every three fractions x < y < z satisfy the Pythagorean equation x^2 + y^2 = z^2: (A268602(3*n-2)/a(3*n-2))^2 + (A268602(3*n-1)/a(3*n-1))^2 = (A268602(3*n)/a(3*n))^2.
The area A = x*y/2 of these Pythagorean triangles is a congruent number: A003273(n) = (1/2) * A268602(3*n-2)/a(3*n-2) * A268602(3*n-1)/a(3*n-1)).
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LINKS
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EXAMPLE
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The first congruent number is 5 and the associated right triangle with the side lengths x = 3/2, y = 20/3, z = 41/6 satisfies the Pythagorean equation (3/2)^2 + (20/3)^2 = (41/6)^2 and the area of this triangle equals 1/2*3/2*20/3 = 5.
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CROSSREFS
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KEYWORD
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nonn,frac,tabf,more
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AUTHOR
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EXTENSIONS
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a(14) corrected on Mar 14 2020
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STATUS
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approved
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