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
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