HMMT 二月 2004 · 冲刺赛 · 第 26 题
HMMT February 2004 — Guts Round — Problem 26
题目详情
- [9] How many of the integers 1 , 2 , . . . , 2004 can be represented as ( mn + 1) / ( m + n ) for positive integers m and n ?
解析
- How many of the integers 1 , 2 , . . . , 2004 can be represented as ( mn + 1) / ( m + n ) for positive integers m and n ? Solution: 2004 2 For any positive integer a , we can let m = a + a − 1 , n = a + 1 to see that every positive integer has this property, so the answer is 2004.