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September 10th, 2017, 05:42 AM   #1
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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.
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September 10th, 2017, 10:29 AM   #2
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Quote:
Originally Posted by phillip1882 View Post
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...
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