1. The problem statement, all variables and given/known data This is taken from an answer book that I have. I don't understand the bolded step. Can someone explain it to me? Suppose x = p/q where p and q are natural numbers with no common factor. Then: pn/qn + an-1pn-1/qn-1 + ... + ao = 0 and multiplying both sides by qn gives pn + an-1pn-1q + ... + aoqn = 0 Now if q ≠ ±1 then q has some prime number as a factor. This prime number divides every term of the second equation other than pn, so it must divide pn also. Therefore it divides p, a contradiction. So q = ±1, which means that x is an integer. Once again, it's the bolded step that I don't understand. Why must it divide pn? Thanks in advance.