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Polynomial with integer coefficients - Paenza 2010

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August 26, 2010
algebrapolynomialalgebra unsolved

Problem Statement

A polynomial ff with integer coefficients is written on the blackboard. The teacher is a mathematician who has 33 kids: Andrew, Beth and Charles. Andrew, who is 77, is the youngest, and Charles is the oldest. When evaluating the polynomial on his kids' ages he obtains: f(7)=77f(7) = 77 f(b)=85f(b) = 85, where bb is Beth's age, f(c)=0f(c) = 0, where cc is Charles' age. How old is each child?
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