- #1
LaMantequilla
- 8
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Homework Statement
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.