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HMMT 十一月 2008 · 冲刺赛 · 第 10 题

HMMT November 2008 — Guts Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 8 ] Find the sum of all positive integers n such that n divides n + n + 2.
解析

英文解析

  1. [ 8 ] Find the sum of all positive integers n such that n divides n + n + 2.
    Answer: 3 Since n always divides n + n , the only n that work are divisors of 2, because if n divides 2
    a and n divides b , then n divides a + b . So the solutions are 1 and 2 which sum to 3.