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HMMT 二月 2000 · ORAL 赛 · 第 1 题

HMMT February 2000 — ORAL Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [25] Find all integer solutions to m = n + 1.
    10 9 8 7 6
解析

英文解析

  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 arem = ± 1 , n = 0.
    6 4 3 2