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HMMT 十一月 2013 · 冲刺赛 · 第 5 题

HMMT November 2013 — Guts Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] How many positive integers less than 100 are relatively prime to 200? (Two numbers are relativelyprime if their greatest common factor is 1.)
解析

英文解析

  1. [ 6 ] How many positive integers less than 100 are relatively prime to 200? (Two numbers are relativelyprime if their greatest common factor is 1.)
    Answer: 40 1 ≤ n < 100 is relatively prime to 200 if and only if it’s relatively prime to 100
    1 4
    (200 , 100 have the same prime factors). Thus our answer is φ (100) = 100 = 40.
    2 5