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HMMT 二月 2000 · ORAL 赛 · 第 1 题

HMMT February 2000 — ORAL Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [25] Find all integer solutions to m = n + 1. 10 9 8 7 6
解析
  1. The equation involves only even powers, so we may assume m, n are positive (negative 6 6 6 3 6 solutions may be generated by switching signs). n ≤ n + 1 ≤ n + 2 n + 1, so n + 1 lies between two squares, with strict inequality unless n = 0. So the only solutions are m = ± 1 , n = 0. 6 4 3 2