A120211 x values giving the smallest integer solutions of y^2 = x*(a^N - x)*( b^N + x) (elliptic curve, Weierstrass equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg a. Relevant y values in A120210.

4, 6, 12, 24, 15, 40, 60, 40, 70, 84, 72, 56, 126, 144, 180, 168, 198, 180, 220, 264, 126, 286, 312, 364, 360, 390, 420, 480, 510, 49, 544, 300, 612, 616, 646, 684, 720, 760, 288, 798, 840, 924, 726, 966, 700, 1012, 1104, 990, 1150, 1200

Offset: 1

Author

Giorgio Balzarotti, Paolo P. Lava, Jun 10 2006

Keywords

• nonn

Examples

			First primitive Pythagorean triad: 3, 4, 5
Weierstrass equation. y^2 = x*( 3^2 - x)*( 4^2 + x)
Smallest integer solution (x, y) = (4,20)
First element in the sequence x = 4
		

References

• G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 47.

Crossrefs

Cf. A009003, A020884, A120210-A120213.

Programs

Maple

flag :=1;x:=0; # a, b, c primitive Pythagorean triad while flag =1 do x:=x+1; y2:= x*( a^2 - x)*(x+b^2); if ((floor(sqrt(y2)))^2=y2)then print( x);flag :=0;fi; od;