【摘要】 本文证明了：如果实值加性函数ｆ（ｎ）满足条件‖ｆ（ｎ＋１）－ｆ（ｎ）‖＝ｏ（１），（ｎ→∞）这里‖‖表示一实数与最近的整数的距离，则一定有某常数ｃ使ｆ（ｎ）一ｃｌｏｇｎ为整数值加性函数．这证实了ＫａｔａｉⅠ的一个猜想．更多还原

【Abstract】 This paper proved that: If real Valued additive functions f(n) satisfies that ‖f(n+1)-f(n)‖=0(1) (n→co), where ‖‖denotes the distance of a real number to the nearest integer,then there exists a suitable constat c such that f(n)-clog n is an integer valned additive function. This confirms a conjecture of Katai Ⅰ.更多还原