PR 4 # 19

Wacky · 2006-06-19, 12:18

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

Chris Card · 2006-06-19, 14:21

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

fetofs · 2006-06-19, 14:57

Quote:

Originally Posted by Chris Card

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

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

2006-06-19, 12:18	#1
Wacky Jun 2003 The Texas Hill Country 3²×11² Posts	PR 4 # 19 Find the simplest solution in integers for the equation $1/x^2 + 1/y^2 = 1/z^2$

2006-06-19, 14:21	#2
Chris Card Aug 2004 2×5×13 Posts	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 Last fiddled with by Chris Card on 2006-06-19 at 14:23