定理两整数的平方差为奇数或4的倍数.证明:m,n∈Z,则 m~2-n~2=(m+n)(m-n),若m、n 一奇一偶,则 m+n、m-n 皆为奇数,其积亦然;若 m、n 同为奇或偶,则 m+n、m-n 皆为偶数,其积自然为2×2=4之倍数.推论1 奇数均可表为相邻整数的平方差.事实上,对任一奇数2k-1,有2k-1=k~2-(k Theorem The square deviation of two integers is odd or multiples of 4. Proof: m, n∈Z, then m ~ 2-n ~ 2 = (m + n) (mn), if m, n is odd and even, then m + n, mn are all odd, the product is also the same; if m, n are odd or even, then m + n, mn are even numbers, the product of natural 2 × 2 = 4 multiple. Corollary 1 odd number can be The table is the square difference of the adjacent integers. In fact, for any odd number 2k-1, there is 2k-1 = k ~ 2- (k