MathDB
f(n + 1)f(n + 2)... f(n + k) / f(1)f(2) ... f(k) \in Z

Source: 2019 Saudi Arabia IMO TST II p2

July 28, 2020
algebrapolynomialdivisible

Problem Statement

Let non-constant polynomial f(x)f(x) with real coefficients is given with the following property: for any positive integer nn and kk, the value of expression f(n+1)f(n+2)...f(n+k)f(1)f(2)...f(k)Z\frac{f(n + 1)f(n + 2)... f(n + k)}{ f(1)f(2) ... f(k)} \in Z Prove that f(x)f(x) is divisible by xx