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HMMT 十一月 2008 · 冲刺赛 · 第 16 题

HMMT November 2008 — Guts Round — Problem 16

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 10 ] If p and q are positive integers and < < , what is the minimum value of p ?
    2009 q 2010
    17
解析

英文解析

  1. [ 10 ] If p and q are positive integers and < < , what is the minimum value of p ?
    2009 q 2010
    Answer: 4017 By multiplying out the fraction inequalities, we find that 2008 q + 1 ≤ 2009 p and
    2010 p + ≤ 2009 q . Adding 2009 times the first inequality to 2008 times the second, we find thatp
    4017
    2008 · 2009 q + 4017 ≤ 2008 · 2009 q + p , or p ≥ 4017. This minumum is attained when = .
    q 4019
    17