OFFSET
1,5
COMMENTS
Triads a = 3, b = 4, c = 5 and a = 4, b = 3, c = 5 provide different results for (x,y).
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
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Jun 22 2006
STATUS
approved