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HMMT 十一月 2016 · 冲刺赛 · 第 23 题

HMMT November 2016 — Guts Round — Problem 23

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 12 ] Let d be a randomly chosen divisor of 2016. Find the expected value of 2 d 2 d + 2016
解析
  1. [ 12 ] Let d be a randomly chosen divisor of 2016. Find the expected value of 2 d 2 d + 2016 Proposed by: Henrik Boecken 1 Answer: 2 Let ab = 2016. Then 2016 2 2 2 2 2 ( ) a b a a 2016 a
  • = + = + = 1 2016 2 2 2 2 2 2 a + 2016 b + 2016 a + 2016 a + 2016 a + 2016 ( ) + 2016 a 1 2016 Thus, every divisor d pairs up with to get 1, so our desired expected value is . d 2