Author Topic: Perfect Squares Problem  (Read 2721 times)

0 Members and 1 Guest are viewing this topic.

Offline Ender

  • Moderator
  • Hero Member
  • *****
  • Posts: 2390
    • View Profile
Perfect Squares Problem
« 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
« Last Edit: July 26, 2007, 01:54:31 am by Ender »

Offline iago

  • Leader
  • Administrator
  • Hero Member
  • *****
  • Posts: 17914
  • Fnord.
    • View Profile
    • SkullSecurity
Re: Perfect Squares Problem
« Reply #1 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

Offline Ender

  • Moderator
  • Hero Member
  • *****
  • Posts: 2390
    • View Profile
Re: Perfect Squares Problem
« Reply #2 on: July 26, 2007, 01:41:51 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
« Last Edit: July 26, 2007, 01:45:03 am by Ender »

Offline iago

  • Leader
  • Administrator
  • Hero Member
  • *****
  • Posts: 17914
  • Fnord.
    • View Profile
    • SkullSecurity
Re: Perfect Squares Problem
« Reply #3 on: July 26, 2007, 08:55:35 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!