試說明:對於任意自然數n,n(n+5)-(n-3)(n+2)的值能被6整除.

試說明:對於任意自然數n,n(n+5)-(n-3)(n+2)的值能被6整除.

∵n(n+5)-(n-3)(n+2)=(n2+5n)-(n2-n-6)=n2+5n-n2+n+6=6n+6=6(n+1)又n≥1∴總能被6整除.