Number Theory Number Theory Math Forum

 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 Tags confused Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post charlieboon Calculus 5 February 23rd, 2013 11:01 AM ccfoose Algebra 3 April 16th, 2012 10:55 PM Siedas Algebra 9 March 10th, 2012 02:29 PM momoftwo New Users 4 August 19th, 2009 07:15 PM charlieboon Algebra 0 December 31st, 1969 04:00 PM

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