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HMMT 二月 1998 · 代数 · 第 4 题

HMMT February 1998 — Algebra — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Given that r and s are relatively prime positive integers such that = , s 5 ( ( 3 + 5 ) find r and s .
解析
  1. Problem: Given that r and s are relatively prime positive integers such that = , find r √ s 5( 3+ 5) and s . √ √ 2 4(12+4 5) 16(3+ 5) r 16 √ √ Solution: Squaring both sides of the given equation yields = = = . Because r 2 s 25 25(3+ 5) 25(3+ 5) and s are positive and relatively prime, then by inspection, r = 4 and s = 5 .