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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.

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    $\begingroup$ See PolynomialExtendedGCD, esp. under "Applications." $\endgroup$ – Michael E2 Feb 28 '18 at 0:07
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    $\begingroup$ Posting the explicit polynomials would help; it might also help to talk a bit more about what you've tried. $\endgroup$ – Pillsy Feb 28 '18 at 3:34

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