整数的离散性是指:任何两个不同整数x、y之间的距离至少为1 ,即|x -y|≥1。从而得到x y x≥y +1。例1　设a、b、c、d、n都是正整数,n 1 ,且a +c≤n ,ab +cd 1①求证:ab +cd 1 -1n3。证　由对称性,不妨设b≥d ,由题设1 -ab -cd =bd -ad -bcbd 0 ,故bd -ad -bc0 ,从而bd - The discreteness of the integer means that the distance between any two different integers x and y is at least 1, ie, |x -y|≥1. This gives x y x≥y +1. Example 1 Let a, b, c, d, and n be positive integers, n 1, and a +c ≤ n, and ab +cd 11 verify: ab +cd 1 -1n3. Prove the symmetry, may wish to set b≥d, by the question set 1 -ab -cd =bd -ad -bcbd 0, so bd -ad -bc0, thus bd -