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September 10th, 2014, 08:36 AM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  find the remainder
The rest of the divisible 3^99 divide by 8 
September 10th, 2014, 08:46 AM  #2 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230 
Check out this link : http://www.wolframalpha.com/input/?i=%283^%2899%29%29%2F8 
September 10th, 2014, 08:52 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra 
$$3^{99} \equiv 3(3^2)^{49} \equiv 3\cdot 9^{49} \equiv 3 \cdot 1^{49} \equiv 3 \cdot 1 \equiv 3 \pmod 8$$
Last edited by v8archie; September 10th, 2014 at 08:58 AM. 
September 10th, 2014, 09:04 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra  
September 10th, 2014, 09:36 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  

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