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HMMT 二月 2007 · TEAM1 赛 · 第 2 题

HMMT February 2007 — TEAM1 Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 20 ] Solve for the positive integer(s) n such that φ ( n ) = 1000 φ ( n ) .
解析
  1. [ 20 ] Solve for the positive integer(s) n such that φ ( n ) = 1000 φ ( n ) . Answer: 1000 . Solution. The unique solution is n = 1000 . For, φ ( pn ) = pφ ( n ) for every prime p dividing n , so that 2 φ ( n ) = nφ ( n ) for all positive integers n.