设n为整数,则2n代表偶数.由1,2得;(2n+1)^2-(2n-1)^2=4n^2+4n+1-4n^2+4n-1=8n
由4 当n=3时 (2n+3)^2-(2n-3)^2=4n^2+12n+9-4n^2+12n-9=24n=8*3n
由3 当n=5时 (2n+5)^2-(2n-7)^2=4n^2+20n+25-4n^2+28n-49=48n-24=8(6n-3).
综上所述:任何两个奇数的平方差都是8的倍数
设n为整数,则2n代表偶数.由1,2得;(2n+1)^2-(2n-1)^2=4n^2+4n+1-4n^2+4n-1=8n
由4 当n=3时 (2n+3)^2-(2n-3)^2=4n^2+12n+9-4n^2+12n-9=24n=8*3n
由3 当n=5时 (2n+5)^2-(2n-7)^2=4n^2+20n+25-4n^2+28n-49=48n-24=8(6n-3).
综上所述:任何两个奇数的平方差都是8的倍数