I'm pretty new to mathematica and am trying to solve the following:
I have two explicit polynomials $f(x), g(x)$ with integer coefficients and a constant $c$ and I'm looking for two polynomials $F(x), G(x)$ such that $$F(x)f(x)+G(x)g(x)=c$$
I was hoping I could do this with
solve[...] but no luck, it seems that will only give me roots of equations. I have a few systems like this I need to solve, so I've been trying to avoid explicit working out the coefficients and solving for them.