Monday, 31 October 2016

contest math - Polynomial P(a)=b,P(b)=c,P(c)=a




Let a,b,c be 3 distinct integers, and let P be a polynomial with integer coefficients.Show that in this case the conditions P(a)=b,P(b)=c,P(c)=a cannot be satisfied simultaneously.



Any hint would be appreciated.


Answer



Hint: If P(a)=b and P(b)=c then ab divides bc.


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