OFFSET
1,2
COMMENTS
For Pythagorean triples (x, y, z) satisfying x^2 + y^2 = z^2, we have 3 and 4 dividing either of x or y and 7 dividing x, y or (x^2 - y^2), so that 3*4*7 always divide x*y*(x^2 - y^2); if (x, y) be themselves the generators of another Pythagorean triple, (x^2 - y^2, 2*x*y, x^2 + y^2=z^2), the corresponding primitive Pythagorean triangle has area x*y*(x^2 - y^2) and is hence divisible by 84.
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jul 11 2002
EXTENSIONS
Corrected and extended by Ray Chandler, Oct 28 2003
Sorted by increasing square hypotenuse, then increasing area by Sean A. Irvine, Sep 20 2024
STATUS
approved