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 Go for short! (Posted on 2005-04-19)
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.

 Submitted by e.g. Rating: 2.0000 (2 votes) Solution: (Hide) All odd numbers are 4K±1, which squared produces 16K²±8K+1, which obviously is a multiple of 8, plus 1.

 Subject Author Date re: my way broll 2016-06-24 23:39:48 my way Ady TZIDON 2012-08-07 12:55:59 If two lines were allowed in the proof...... K Sengupta 2008-12-17 06:09:53 Puzzle Solution K Sengupta 2008-12-16 13:19:13 "computer" solution Duncan Garp 2005-06-04 05:34:12 Solution Michael Cottle 2005-04-19 18:29:51 Another way Federico Kereki 2005-04-19 12:43:14 How about this? Bractals 2005-04-19 11:08:36

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