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HMMT 十一月 2008 · GEN1 赛 · 第 4 题

HMMT November 2008 — GEN1 Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 4 ] How many numbers between 1 and 1 , 000 , 000 are perfect squares but not perfect cubes?
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解析

英文解析

  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 andonly 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.
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