Friday, May 4, 2018

algebra precalculus - Proving no polynomial $P(x)$ exists such that $P(a) = b$, $P(b) = c$, $P(c) = a$




If $P(x)$ is a polynomial with integer coefficients and $a, b ,c$ are three distinct integers, then show that it is impossible to have $P(a) = b$, $P(b) = c$, $P(c) = a$.


Answer



Hint: $b-c$ is divisible by $a-b$, and ...


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