Question

求证：两个连续奇数的平方差是8的倍数

Answer 1

设两数为2n-1,2n+1(n为整数)

则(2n+1)^2-(2n-1)^2

=(2n+1+2n-1)*(2n+1-2n+1)

=4n*2

=8n

故其一定是8的倍数