Suppose a1,a2,…,an are different Integers of n-1. This paper proves that if n≥4, the polynomial f(x)=(x-a1)(x-a2)…(x-an)-1 is irreducible in the rational number range Q, and if n≥3, the polynomial f(x)=(x-a1)2(x-a2)2…(x-an)2+1 is irreducible in the rational number range Q.