PETS/SAT (0009)

来源：百度知道 编辑：UC知道 时间：2024/05/25 15:49:54
PETS/SAT (0009)
Show that the sum of the square of any four consecutive odd numbers is divisible by 4?

Solutions:let the 4 consecutive odd number are (2x-1)、(2x+1)、(2x-3)、(2x+3)
so (2x-1)²+(2x+1)²+(2x-3)²+(2x+3)²
Contractions have 16x²+20
becase 16 and 20 are divisible by 4.
so when x=?（x≠0）
eg:when x=1, so the 4 consecutive odd number are 1、3、-1、5.
…… ………………