We have this assignment in programming class, but I believe posting it in math will make more sense.
So we're supposed to write a program that takes $n$ equations with each $n$ coefficients, $n\leq10$, as well as 'a value for mod' and then solves the whole thing. Coefficients are supposed to be in $\mathbb{Z}_p^*$, but I don't really know what that is.
Now I have two things I'm not sure about:
how exactly is that with the mod supposed to work? I never saw something like that before, just common Gauss elimination. I also heard it only makes sense when the mod value is prime. So how to handle a non-prime mod value?
if I have less than $n$ equations left, how could I determine how many solutions the system has?
Thank you for any help.
Edit: to help my understanding of how the process works:
Let's say I have $1x+2y=3 \mod5$ and $2x+3y=4\mod 5$. The result is supposed to be $(4,2)$.
Also, for $1x+2y=4 \mod4$ and $3x+4y=5 \mod4$ the prof's example program crashes. What is going on there that he missed to pay attention to?