Let a(x) and b(x) be in F[x]. I need to prove that if a(x) and b(x) determine the same function, and if the number of elements in F exceeds the degree of a(x) as well as the degree of b(x), then a(x) = b(x).

I know what if a(x) and b(x) determine the same function means. It means that a(x) - b(x) gives you the zero function. I dont know what if the number of elements in F exceeds the degree of a(x) as well as the degree of b(x) means. I also do not see how either of the two can conclude a(x) = b(x). Can anyone help me?