MathDB
Polynomial

Source: Greek TST 2005-pr3

September 30, 2005
algebrapolynomialalgebra proposed

Problem Statement

Let the polynomial P(x)=x3+19x2+94x+aP(x)=x^3+19x^2+94x+a where a∈Na\in\mathbb{N}. If pp a prime number, prove that no more than three numbers of the numbers P(0),P(1),…,P(p−1)P(0), P(1),\ldots, P(p-1) are divisible by pp.
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