Prove property of diophantine equation

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

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