关于平方根整数部分的一个恒等式的推广

Generalization for the Identity on the Integral Parts of Square Roots

设a,b都是正整数.本文证明了:对不小于b+2/2的正整数m,n,若f(n)=[1/2((a+n2-b)～(1/2))]+[1/2(a-n)],g(m)=[1/2(a-((m2-b)～(1/2))]+[1/2(a+m)],则必有f(n)=g(m).

Let and b are positive integers.In this paper we prove that for any positive integers and,with m,n≥b＋2/2,if f（n）=[1/2（（a＋n2-b）～（1/2））]＋[1/2（a-n）],g（m）=[1/2（a-（（m2-b）～（1/2））]＋[1/2（a＋m）] ,then f（n）=g（m）.