求证3个连续自然数的立方和能被9整除

a^3+(a+1)^3+(a-1)^3=a^3+a^3+3a^2+3a+1+a^3-3a^2+3a-1=3a^3+6a=3a(a^2+2)1.a=3n则原式可被9整除2.a=3n+1 ,3a可被3整除,a^2+2=9n^2+6n+3=3(3n^2+2n+1)也可被3 整除3.a=3n+2,a^2+2=9n^2+12n+6=3(3n^2+6n+2)也可被3整...