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A120336
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Number of solutions (x,y) of Diophantine equation y^2 = x*(a^N - x)*( b^N + x) ( Weierstrass elliptic equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg "a".
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0
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1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Triads a = 3 b = 4 c = 5 and a = 4 b = 3 c = 5 provide different results for (x,y).
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EXAMPLE
| First primitive Pythagorean triad: 3, 4, 5
Weierstrass equation. y^2 = x*( 3^2 -x)*( 4^2 + x)
Unique integer solution (x,y) = (4,20)
First element in the sequence = 1
Fifth primitive Pythagorean triad: 8, 15, 17
Integer solutions (x,y) = (15, 420) and (30, 510)
Fifth element in the sequence = 2
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MAPLE
| # a, b, c primitive Pythagorean triad n_sol:=0; for x from 1 by 1 to a^2 do y2:= x*( a^2 - x)*( x+ b^2); if ((floor(sqrt(y2)))^2=y2) n_sol:=n_sol+1; fi; print(n_sol) ; od;
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CROSSREFS
| Cf. A009003, A020884, A120210, A120211, A120212, A120213.
Sequence in context: A165633 A117456 A030621 * A039738 A191515 A168201
Adjacent sequences: A120333 A120334 A120335 * A120337 A120338 A120339
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KEYWORD
| nonn
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AUTHOR
| Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Jun 22 2006
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