由于
n^5+n^4+1=n^5+n^4+n^3-n^3+1=n^3(n^2+n+1)-(n-1)(n^2+n+1)
=(n^2+n+1)(n^3-n+1)
所以,对于任意自然数n>1,n^5+n^4+1是两个自然数的积,故为合数.