Can anyone think of an example of a polynomial f(g) with integer coefficients which factors (poly mod n) but has no roots, e.g. for which there are no such integers g where f(g)=0(mod n) ?
What are appropriate values of n, the coefficients of f(g), and how can I show that it has no roots?
Any help is appreciated!
I'm a little confused about this as you can tell...
And from what you and wonderboy are discussing, I take it that when we say there are no roots, we mean that there are no REAL roots? no integer roots? Both?