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HMMT 二月 2000 · ORAL 赛 · 第 3 题

HMMT February 2000 — ORAL Round — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [35] Suppose the positive integers a, b, c satisfy a + b = c , where n is a positive integer greater than 1. Prove that a, b, c > n . (Note: Fermat’s Last Theorem may not be used)
解析
  1. Assume w.lo.g that c > b ≥ a . Then c − b = ( c − b )( c + ... + b ) > 1( nb ) ≥ n − 1 n n − 1 na . So a > na , hence a > n .