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HMMT 二月 2009 · GEN1 赛 · 第 1 题

HMMT February 2009 — GEN1 Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 2 ] If a and b are positive integers such that a − b = 2009, find a + b .
解析
  1. [ 2 ] 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 that a = 45 and b = 2 is a possible solution. By examining the factors of 2009, one can see that there are no other solutions.