HMMT 二月 2003 · GEN1 赛 · 第 4 题
HMMT February 2003 — GEN1 Round — Problem 4
题目详情
英文原题
- How many 2-digit positive integers have an even number of positive divisors?
解析
英文解析
- How many 2-digit positive integers have an even number of positive divisors?
Solution: 84
An integer has an odd number of divisors precisely if it is a square. So we take the 90
2 2 2
2-digit numbers (10 , 11 , . . . , 99) and remove the 6 squares (4 , 5 , . . . , 9 ), for a total of