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HMMT 二月 2003 · GEN1 赛 · 第 4 题

HMMT February 2003 — GEN1 Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. How many 2-digit positive integers have an even number of positive divisors?
解析
  1. 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