Originally Posted by

**JaysFan31** Had the following question:

If r is in Z and r is a non-zero solution of x^2+ax+b=0 (where a,b are in Z) prove that r divides b.

I solved it the following way:

Letting c and r be the roots of the polynomial.

(x-c)(x-r)=0

x^2+x(-r-c)+cr=0

cr=b, which is the definition of r dividing b

The question then goes on by saying:

Determine for which natural numbers n the polynomial Pn(x)=(x^n)+(x^n-1)+....x+1 has integer roots and find them. (By an integer root we mean z in Z such that f(z)=0). Give two solutions for the problem

1) By proving a suitable generalization of the already said theorem above.

2) By using complex numbers and the polynomial x^(n+1)-1

Yeah I have no idea what to do here. Any help appreciated.