返回题库

HMMT 十一月 2008 · GEN1 赛 · 第 4 题

HMMT November 2008 — GEN1 Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] How many numbers between 1 and 1 , 000 , 000 are perfect squares but not perfect cubes? √
解析
  1. [ 4 ] How many numbers between 1 and 1 , 000 , 000 are perfect squares but not perfect cubes? 2 6 Answer: 990 1000000 = 1000 = 10 . A number is both a perfect square and a perfect cube if and only if it is exactly a perfect sixth power. So, the answer is the number of perfect squares, minus the number of perfect sixth powers, which is 1000 − 10 = 990. √