Clan x86

General Forums => Academic / School => Math and Other Problems => Topic started by: Ender on July 25, 2007, 10:50:59 pm

Title: Perfect Squares Problem
Post by: Ender on July 25, 2007, 10:50:59 pm

Find all x such that x^2 + 2 is a perfect square.

EDIT1: x is an integer, as assumed with all number theory problems

EDIT2: iago just answered correctly -- it holds for no integer values of x. Now prove it :-o

Title: Re: Perfect Squares Problem
Post by: iago on July 26, 2007, 12:02:07 am

I could be wrong, but I can't imagine that holding for any value. At least, for any integer value. Unless, of course, you mean xor and not exponent, since "^" is pretty ambiguous :P

Title: Re: Perfect Squares Problem
Post by: Ender on July 26, 2007, 01:41:51 am

Quote from: iago on July 26, 2007, 12:02:07 am

I could be wrong, but I can't imagine that holding for any value. At least, for any integer value. Unless, of course, you mean xor and not exponent, since "^" is pretty ambiguous :P

Yep, it holds for no values of x. Now prove it!

And yeah, ^ means exponent :O

Title: Re: Perfect Squares Problem
Post by: iago on July 26, 2007, 08:55:35 am

Quote from: Ender on July 26, 2007, 01:41:51 am

Quote from: iago on July 26, 2007, 12:02:07 am

I could be wrong, but I can't imagine that holding for any value. At least, for any integer value. Unless, of course, you mean xor and not exponent, since "^" is pretty ambiguous :P

Yep, it holds for no values of x. Now prove it!

And yeah, ^ means exponent :O

Well, my proof is that it doesn't hold for -2, -1, 0, 1, or 2, and squares before -2 and after 2 are further than 2 apart so it can't possibly be true. That's probably not the hoity toity proper proof, but it makes sense to me!