|
|
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
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 47.
|
|
LINKS
|
|
|
EXAMPLE
|
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
|
|
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;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|