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.
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.