Given primes ,, and a pair (,), how can we find the smallest (≥0) such that = mod and = mod .
Given several pairs of mod values, can these be sorted in the right order?
At the very least, I would like to know the smallest number.
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FYI, see Chinese remainder theorem. – John Omielan Feb 11 '25 at 01:53
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I do not see a way of sorting the modulo pairs without actually first computing the corresponding numbers. I would at least like to know which modulo pair corresponds to the smallest number? Please do not close the question yet. – mmk Feb 11 '25 at 02:43
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1Generally it is not possible to immediately determine that ordering from the modular values w/o computing the value. – Bill Dubuque Feb 11 '25 at 03:38