Thanks for the tip and the additional explanation!
Quote:
Originally Posted by LaurV
This also proves that it is enough for two polynomials of degree n to be the same in n+1 values (as they have n+1 coefficients), to be the same in all their domain. (i.e. if two polynomials of degree n in R have the same values in n+1 points, they are the same in all R, following a similar procedure, and induction).

Exactly  and the point in Number Theory is that we may not
have n+1 distinct values, e.g. in the integers modulo n.