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PUMaC 2012 · 数论（A 组） · 第 5 题

PUMaC 2012 — Number Theory (Division A) — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 5 ] Call a positive integer x a leader if there exists a positive integer n such that the decimal n 3 representation of x starts (not ends) with 2012. For example, 586 is a leader since 586 =
  2. How many leaders are there in the set { 1 , 2 , 3 , ..., 2012 } ? p n − 1
解析
  1. [ 5 ] Call a positive integer x a leader if there exists a positive integer n such that the decimal n 3 representation of x starts (not ends) with 2012. For example, 586 is a leader since 586 =
  2. How many leaders are there in the set { 1 , 2 , 3 , ..., 2012 } ? Solution: We see that x is a leader if and only if there exists a positive integer t such that s n s