Prove property of diophantine equation

1. Oct 17, 2004

ascheras

Show that the diophantine equation x^2 - y^2= n is solvable in integers iff n is odd or 4 divides n.

2. Oct 18, 2004

ZeAsYn51

Well, 4^2-3^2=7 and 4^2-2^2=12, 12/4=3.

3. Oct 19, 2004

matt grime

That isn't a proof. That is an example.

Consider the answer mod 4, one only needs to show n =2 mod 4 can't happen, which is straight forward.

4. Oct 19, 2004

Gokul43201

Staff Emeritus
And it becomes all the more obvious if you write x = y + k, for some integer k.

Edit : Well, maybe not...but it doesn't make it harder.

Last edited: Oct 19, 2004