Hello I'm trying to prove the following conjecture, Any positive integer can be expressed in the form where a positive integer and or . Any ideas ?
Last edited by Raoh; Feb 27th 2011 at 03:55 PM.
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It seems likely but difficult to prove. Did you make this up for fun?
Originally Posted by Bruno J. Bah! I'm going to bed! Thanks for the catch. -Dan
@Bruno.J No i didn't make anything up.
i've found a hint, i will come to discuss it later.I'm off =)
Originally Posted by Raoh i've found a hint, i will come to discuss it later.I'm off =) 2 = -1^2 - 1^2 + 2^2 5 = -2^2 + 3^2 6 = 1^2 + 1^2 + 2^2
Originally Posted by Wilmer 2 = -1^2 - 1^2 + 2^2 5 = -2^2 + 3^2 6 = 1^2 + 1^2 + 2^2 Yes,but that's not what the conjecture states
Right...my bad...but: -1 - 4 + 9 = 4 1 - 4 - 9 + 16 = 4 My point? More than 1 solution...
This thread deserves to be moved in Number Theory!
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