January 22nd, 2009, 08:07 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, 05:08 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, 07:08 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 

Tags 
confused 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
So confused with this  charlieboon  Calculus  5  February 23rd, 2013 10:01 AM 
confused. please help!  ccfoose  Algebra  3  April 16th, 2012 09:55 PM 
I am a little Confused.  Siedas  Algebra  9  March 10th, 2012 01:29 PM 
I am new and confused....  momoftwo  New Users  4  August 19th, 2009 06:15 PM 
So confused with this  charlieboon  Algebra  0  December 31st, 1969 04:00 PM 