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Question regarding mod classes

by CalculusSandwich
Tags: classes
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Feb26-12, 03:51 AM
P: 18
Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives
a remainder of 4 in each case.

I know I can approach this problem by writing the equivalence classes.

x=4mod45 or x=4mod70

I also know I can find x by multiplying 12*17*45 + 4, but this isn't the smallest positive integer.

Can someone help me with a formula I can use?
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Feb26-12, 06:33 AM
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P: 6,189
Erm... how about the solution x=4?
It is a solution and I don't think there are any smaller positive integers that are also a solution.
Feb26-12, 01:32 PM
P: 144
If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.

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