Hello All,

My book states the following:

[PART ONE]

If 'b' is any integer and the polynomial f(x)=(x^2)+bx+1 factors (poly mod9), there existsdistinct non-negative integers 'q' less than than 9 so that f(q)3=0(mod9).

How can this be proven?

[PART TWO]

If 'b' is any integer and the polynomial f(x)=(x^2)+bx+1 factors (poly mod8), then f(x) is a square. E.g. f(x)=((x+c)^2)(poly mod8) where 0<c<8.

Can anyone think of values of b that makes this possible?