PETS/SAT (0010)

来源：百度知道 编辑：UC知道 时间：2024/06/02 11:18:43
PETS/SAT (0010)
Show that the sum of the square of any three consecutive even numbers is divisible by 4?

Solutions:let the 3 consecutive even numbers are (2x-2)、2x、(2x+2)

so，the sum of the square of each are S=(2x-2)²+(2x+2)²+（2x）²

After simplification：S=12x²+8=4【3x²+2】is divisible by 4.

Shown.