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HMMT 二月 2001 · 代数 · 第 4 题

HMMT February 2001 — Algebra — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Given that 7 , 999 , 999 , 999 has at most two prime factors, find its largest prime factor.
解析

英文解析

  1. Given that 7 , 999 , 999 , 999 has at most two prime factors, find its largest prime factor.
    9 3 2
    Solution: 7 , 999 , 999 , 999 = 8 · 10 − 1 = 2000 − 1 = (2000 − 1)(2000 + 2000 + 1), so
    (2000 + 2000 + 1) = 4,002,001 is its largest prime factor.2