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: bc is divisible by ab, and ...


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