January 22nd, 2009, 09:07 PM  #1 
Member Joined: Jan 2009 Posts: 30 Thanks: 0  so confused here...
ok this is the problem/question Show that the square of an odd integer is of the form 8k +1 for some k in a set of integers. so like....how do u even start this problem???? all i know is that i need to do a proof 
January 23rd, 2009, 06:08 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: so confused here...
Try each of the possibilities mod 8. There are only 4.

January 23rd, 2009, 08:08 AM  #3 
Senior Member Joined: Dec 2008 Posts: 160 Thanks: 0  Re: so confused here...
Steps: 1. Any odd integer has form O = 2k + 1. 2. Square of it is O^2 = 4k(k + 1) + 1. 3. If k = 2n, then O^2 = 8n(2n + 1) + 1 = 8m + 1 4. If k = 2n + 1, then O^2 = 8(n + 1)(2n + 1) + 1 = 8p + 1 

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