Polynomial but rearranged
Let be a polynomial with integer coefficients such that and . Does the polynomial have integer roots ?
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1 solution
Since a − b ∣ a n − b n for distinct integers a and b and integer n ≥ 1 , it follows that (for a = b ), a − b ∣ f ( a ) − f ( b ) .
Let's say r is an integer root of f . Then applying the above with the given information, both
r ∣ 2 0 1 9 and r − 1 ∣ 9 0 2 1
have to hold. But checking the divisors (positive and negative) of these shows that no such r exists.