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HMMT 二月 2009 · 冲刺赛 · 第 18 题

HMMT February 2009 — Guts Round — Problem 18

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 9 ] Find the positive integer n such that n + 2 n + 9 n + 8 is the cube of an integer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . th 12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUND
解析
  1. [ 9 ] If n is a positive integer such that n + 2 n + 9 n + 8 is the cube of an integer, find n . Answer: 7 3 3 2 3 3 2 3 Solution: Since n < n + 2 n + 9 n + 8 < ( n + 2) , we must have n + 2 n + 9 n + 8 = ( n + 1) . 2 Thus n = 6 n + 7, so n = 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . th 12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUND