My Math Forum modular arithmetic question

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 September 10th, 2017, 04:42 AM #1 Member   Joined: May 2013 Posts: 34 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, 09:29 AM   #2
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Quote:
 Originally Posted by phillip1882 8611 cong to 75 mod 97 and 8611 cong to 26 mod 101 and a*b = 8611, what are a and b?
8611 @ 97 = 75
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...

 Tags arithmatic, arithmetic, modular, question

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