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September 10th, 2017, 05:42 AM  #1 
Member Joined: May 2013 Posts: 33 Thanks: 1  modular arithmetic question
it seems to me we should be able to factor a number based on remainders. ie if 8611 cong to 75 mod 97 and 8611 cong to 26 mod 101 and a*b = 8611, what are a and b? but i don't see an easy way to approach it. 
September 10th, 2017, 10:29 AM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,909 Thanks: 716  Quote:
8611 @ 101 = 26 8611 = a*b Well, you can let b = a + k, to get quadratic: a(a + k) = 8611 a^2 + ka  8611 = 0 I'm sure you tried: 97u + 75 = 101v + 26 : little or no help! I simply can't see a unique solution... perhaps someone else will...  

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arithmatic, arithmetic, modular, question 
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