A primitive Pythagorean triangle (PPT) is a right triangle whose side lengths are integers that are relatively prime.

1) Prove that the inradius of a PPT has a different parity than the mean of the hypotenuse and the odd leg.

2) Prove that there exists an infinite number of pairs of non-congruent PPTs such that both members of the pair have the same inradius.

(In reply to solution by Daniel)

One nitpik. At the beginning you gave m>n and m,n coprime as restrictions on m and n. In Part 1) you used the further restriction (which I agree is needed) that m and n are of different parity.

Posted by Bractals on 2008-01-26 17:00:04