|
| |
|
|
A120210
|
|
Integer squares y from the smallest solutions of y^2 = x*(a^N - x)*( b^N + x) (elliptic line, Weierstrass equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg a.
|
|
3
| |
|
|
20, 30, 156, 600, 420, 1640, 3660, 520, 2590, 7140, 1224, 10920, 8190, 20880, 32580, 4872, 19998, 5220, 48620, 69960, 3150, 41470, 97656, 132860, 19080, 76830, 176820, 230880, 131070, 12740, 296480, 11100, 375156, 52360, 209950, 468540, 64080
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The case x congruent to 0 mod b or b congruent to 0 mod x is frequent (e.g. A120212). Note that the triads a = 3 b = 4 c = 5 and a = 4 b = 3 c = 5 provide a different result for (x, y).
The natural solution is y = c * b * (c-b) and x = b * (c-b) with c hypotenuse in the triad - Giorgio Balzarotti (greenblue(AT)tiscali.it), Jul 19 2006
|
|
|
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 y = 20
|
|
|
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( sqrt(y2)); flag :=0; fi; od;
|
|
|
CROSSREFS
| Cf. A009003, A020884, A120211, A120212, A120213.
Sequence in context: A142342 A008444 A066214 * A181639 A166631 A167360
Adjacent sequences: A120207 A120208 A120209 * A120211 A120212 A120213
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Giorgio Balzarotti, Paolo P. Lava (greenblue(AT)tiscali.it), Jun 10 2006
|
| |
|
|
