The problem statement:

Notice that need NOT be pairwise coprime.Let . Prove that there is a unique of degree such that for all . [Hint: Use the Chinese remainder theorem.]

It seems to me that this problem is equivalent to showing that the linear system , where

, and ,

has exactly one solution, which in turn is equivalent to showing that is invertible.

However, the hint tells me to use the Chinese remainder theorem---and I don't see how that's relevant.

Any help would be much appreciated. Thanks!