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PUMaC 2014 · 几何（A 组） · 第 1 题

PUMaC 2014 — Geometry (Division A) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 3 ] Let x = for p, q coprime. Find p + q q
解析
  1. [ 3 ] Let x = for p, q coprime. Find p + q q Solution: z 4 AEF 4 AEB Let S 4 ADF = y and S 4 AEF = z . Hence x = y + z . We see that = = = 2 4 CEF 4 CEB y + z + 3 y 4 ADF 4 ADC y + z + 2 9 8 and = = = . Solving, we see that z = and y = . 8 3 4 BDF 4 BDC 9 5 5 17 Thus x = and hence p + q = 22 . 5