Ok, let be one of those monic quadratics which is alsoirreducible( can you prove such a thing mustexist? Note that according to whatalways

you said you can!)) , so that the ideal is maximal in (why?) the factor ring is a field (why?) .

Well, now just prove that ...

Hint: every element in as defined above has the form , but using Euclides algorithm in show that any element in has a

representative with and any two of them is a different element in the field.

Well, now just count up all the different constant and linear poilynomials in ...

Tonio