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HMMT 二月 2009 · 代数 · 第 1 题

HMMT February 2009 — Algebra — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] If a and b are positive integers such that a − b = 2009, find a + b .
    2009
解析

英文解析

  1. [ 3 ] If a and b are positive integers such that a − b = 2009, find a + b .
    Answer: 47
    2 2
    Solution: We can factor the equation as ( a − b )( a + b ) = 41 · 49, from which it is evident thata = 45 and b = 2 is a possible solution. By examining the factors of 2009, one can see that there areno other solutions.
    2009