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Go for short! (Posted on 2005-04-19) Difficulty: 2 of 5
Looking at the "Square of an Odd" puzzle that asks to prove that the square of an odd number is always 1 more than a multiple of 8, a professor gave this four parts proof: "All odd numbers are of the form 8K+1, 8K+3, 8K+5 or 8K+7. Squaring these numbers produces 8M+1, 8M+9, 8M+25 or 8M+49, which are all of the form 8N+1. QED"

Another professor came by, and gave a single line proof. Can you manage it?

Note: no one who answered the original problem produced either the four parts solution, or the single line one.

See The Solution Submitted by e.g.    
Rating: 2.0000 (2 votes)

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Solution Solution | Comment 3 of 8 |
2n+1 is the odd number
(2n+1)²=4(n²+n)+1
n²+n is a multipule of 2 for all n integers greater than 0

Therefore the odd number squared is a multipule of 8 plus 1.
  Posted by Michael Cottle on 2005-04-19 18:29:51
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