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A120336 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". 0
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; text; internal format)
OFFSET

1,5

COMMENTS

Triads a = 3, b = 4, c = 5 and a = 4, b = 3, c = 5 provide different results for (x,y).

LINKS

Table of n, a(n) for n=1..78.

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.

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;

CROSSREFS

Cf. A009003, A020884, A120210, A120211, A120212, A120213.

Sequence in context: A117456 A030621 A284582 * A284558 A294623 A039738

Adjacent sequences:  A120333 A120334 A120335 * A120337 A120338 A120339

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti and Paolo P. Lava, Jun 22 2006

STATUS

approved

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)