I was specifically looking for a program that can solve congruences, but a program that can solve a system of congruences would be amazing.

For example:

x == 2 mod 3
x == 3 mod 5
x == 4 mod 11

or any number theory program would be helpful.

Thanks (:

Use google.
There are dozens & dozens of code modules available (for the stealing, or free) and in different computer languages to answer your number theory problems.

All you have to do is assemble the fragments into a working program.

It is far more instructive to construct your own. If you build the code, you will have a better comprehension of the algorithm.

What computer programming language do you prefer?

I would not be surprised if "Pari" can do that, and in honor of Descartes, I'll leave that for you to discover.

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