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?

(In reply to People seem to be wrong... by Euan)

A "Pythagorean Plus One" triple is not defined as being a pythagorean triple.  It may seem to imply that it is a pythagorean triple by the name, but it doesn't, that's just what Gamer chose to name it.

As for a triple that is both a "pythagorean plus one" triple and a pythagorean triple, I think it is impossible.

a*b=c
a^2+b^2=c^2
(a*b)^2=a^2+b^2
0=a^2+b^2+^2÷b^2
0=(b^2+1)a^2+b^2
a=(0+/-sqrt(0-4b^2(b^2+1)))/2
Notice that in the above line, there is no positive real solution for both a and b.

Edit: Fixed sqrt sign and sqr signs

Edited on June 4, 2004, 10:33 pm

Posted by Tristan on 2004-06-04 18:11:26