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Princeton's Prime Problem (Posted on 2002-11-18) Difficulty: 3 of 5
Prove that every prime number other than 2, can be expressed as a difference of two squares.

- Princeton Math Club Website

See The Solution Submitted by Raveen    
Rating: 3.7273 (11 votes)

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Solution puzzle solution | Comment 7 of 9 |
Any given prime number other than 2 (m, say)must be odd.
Thus, we can substitute m = 2x+1.
Since, m>=3, it follows that x>=1.

Now, 
m =  2x+1
= (x+1)^2 - x^2, where x>=1
  
Consequently, any given prime number other than 2 ia always expressible as the difference of two squares.

Edited on January 23, 2008, 10:37 am
  Posted by K Sengupta on 2007-05-18 15:10:06

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