N〔N+5〕—〔N—3〕×〔N+2〕
=N^2+5N-(N^2-N-6)
=N^2+5N-N^2+N+6
=6N+6
=6(N+1)
所以对任何自然数N,代数式N〔N+5〕—〔N—3〕×〔N+2〕的值都能被6整除