A "Pythagorean Plus One" triple can be defined as any three distinct integers a, b, c, such all three of these are one more than a perfect square, and also a times b equals c.
What is the lowest value of c possible?
If you write a=x^2+1, b=y^2+1, c=z^2+1, then if c=ab we find that
x^2y^2+x^2+y^2 = z^2 and we can write z^2x^2y^2 = x^2+y^2, or
(z+xy)(zxy)=x^2+y^2.
Plugging in the classic x=3, y=4, we find that z=13, so a=10, b=17, c=170.

Posted by Oskar
on 20040517 08:50:36 