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September 12th, 2010, 04:29 AM  #1 
Newbie Joined: Sep 2010 Posts: 6 Thanks: 0  Largest integer _1
Hi all, I want to find the largest integer that divides 364, 414, and 541 with remainders R1 , R2, and R3, respectively, such that R2 = R1 + 1, and R3 = R2 + I. Can anybody help me to solve the problem?... 
September 12th, 2010, 04:40 AM  #2  
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0  Re: Largest integer _1 Quote:
 
September 12th, 2010, 01:19 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,445 Thanks: 1312 
The answer is the greatest common divisor of 414  364  1 = 49 and 541  414  1 = 126. It's easy to see that gcd(49, 126) = 7. The remainders mentioned are 0, 1, and 2. Had the gcd been less than three, there would have been no solution. 

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