PR 4 # 19
 

Find the simplest solution in integers for the equation [tex]1/x^2 + 1/y^2 = 1/z^2[/tex]

[spoiler]
Let p,q,r be integers such that p^2 + q^2 = r^2
Let x = pr, y = qr and x = pq
Then
1/x^2 + 1/y^2 = 1/z^2
[/spoiler]

[QUOTE=Chris Card][spoiler]
Let p,q,r be integers such that p^2 + q^2 = r^2
Let x = pr, y = qr and x = pq
Then
1/x^2 + 1/y^2 = 1/z^2
[/spoiler][/QUOTE]

[spoiler]Therefore, for:
p = 3
q = 4
r = 5
We have the sol.
x = 15 y =20 z = 12[/spoiler]