设 f (x)是一个整系数多项式 ,如果 f(x)不能分解为两个次数均≥ 1的整系数多项式的乘积 ,那么就称 f(x)在整数环 Z上是不可约的 .下面是第 34届 IMO之第 1题及其标准答案 .设 f(x) =xn +5 xn-1 +3,其中 n是一个大于 1的整数 .求证 :f(x)在整数环 Z上是不可约的 .证明　运用反 Let f(x) be an integer polynomial. If f(x) cannot be decomposed into the product of polynomials of integers with both times ≥ 1, then we say that f(x) is irreducible on the integer ring Z. It is the first question of the 34th IMO and its standard answer. Let f(x) = xn +5 xn-1 +3, where n is an integer greater than 1. Proof: f(x) is on the integer ring Z Irreducible