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PUMaC 2008 · 个人决赛（A 组） · 第 1 题

PUMaC 2008 — Individual Finals (Division A) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Find all positive real numbers b for which there exists a positive real number k such that n − k ≤ b bn c ≤ n for all positive integers n .
解析
  1. Find all pairs of positive real numbers ( a, b ) such that ≤ b bn c < for all positive integers n . a a 1 − 1 ( ANS: None exist. If b > 0, then we have 0 ≤ b b c < = 0, a contradiction. CB: EK) a