August 26th, 2012, 08:45 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Modular Arithmetic
Can anyone shed a little light on this problem? Prove that if is a multiple of 4 then It may help to know that The solution I was given was to use induction 
August 26th, 2012, 09:11 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,164 Thanks: 472 Math Focus: Calculus/ODEs  Re: Modular Arithmetic
I'm not sure about your notation, but I am guessing you are to prove that: where Is this correct? 
August 27th, 2012, 08:34 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Modular Arithmetic Hello, aaronmath! Quote:
 
August 27th, 2012, 08:51 AM  #4 
Senior Member Joined: Mar 2012 Posts: 572 Thanks: 26  Re: Modular Arithmetic
A folksier version: Any number that ends in 1 = 1 mod 10 = 1 mod 5 Any number that ends in 1 x any number that ends in 7 ends in 7. (7^1, 7^5, 7^9...) Any number that ends in 7 x any number that ends in 7 ends in 9. (7^2, 7^6, 7^10...) Any number that ends in 9 x any number that ends in 7 ends in 3. (7^3, 7^7, 7^11...) Any number that ends in 3 x any number that ends in 7 ends in 1. (7^4, 7^8, 7^12...) 

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arithmetic, modular 
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