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P(5) is divisible by 2,P(2) is divisible by 5 then P(7) is divisible by 10

Source: Polish second round 1995 p1

January 19, 2020

Integer Polynomialpolynomialdivisiblealgebra

Problem Statement

For a polynomial

P

with integer coefficients,

P(5)

is divisible by

2

and

P(2)

is divisible by

5

. Prove that

P(7)

is divisible by

10