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I have gotten the task of finding the smallest number which is:

1 or 2 mod 3

0 mod 4

0 or 1 or 4 mod 5

1, 2, 5, 6, 9 or 10 mod 11

I have also been given that the smallest number is in the range [10,50].

Now, it is quite easy to see that 16 is the smallest number creating a solution.

But my question is if there are any known algorithm for finding the smallest possible solution besides lining up all 2*1*3*6 modular equations and solving them?

Thanks

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# Finding smallest solution to modular equations

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