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PUMaC 2017 · 代数（B 组） · 第 3 题

PUMaC 2017 — Algebra (Division B) — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. Let a b = ab − 4( a + b ) + 20. Evaluate 1 (2 (3 ( · · · (99 100) · · · ))) . √ 3
解析
  1. Note that a b = ( a − 4)( b − 4) + 4, so 4 b = a 4 = 4 for any a, b . Since a 4 appears in the expression, the answer is 4 . Problem written by Matt Tyler