Definition Let "F"  be a field with f(x), g(x), p(x) being polynomials in F[x] and "p(x)" nonzero. Then if "p(x)|f(x)-g(x)" we say "f(x)" is congruent to "g(x)" modulo "p(x)". 
               
For example, in Q[x], x^2+x+1 is congruent to x+2 modulo x+1 because （x^2+x+1)-(x+2) = x^2-1=(x+1)(x-1).

This congruence among polynomials is similar, but not quite the same as congruence among integers.

Is there a way, in Maple, to solve problems like this? Could Maple tell me, for example, what polynomials are congruent to x^2+x+1 modulo x+1? An answer might be in the form x^2 +x+1 belongs to [x-1], an  equivalence class of polynomials.

I have not been able to find any such function in Maple, nor any calculator for it on the web. Maybe I'm not using the right search terms.