4

Part of 1997 Greece National Olympiad

Problems(1)

Inequality for a polynomial on Z[x]

Source: Greek national M.O. 1997, Final Round, problem 4

P

with integer coefficients has at least

13

distinct integer roots. Prove that if an integer

n

is not a root of

P

|P(n)| \geq 7 \cdot 6!^2

, and give an example for equality.

inequalitiesalgebrapolynomialnumber theory unsolvednumber theory