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HMMT 二月 2007 · 冲刺赛 · 第 5 题

HMMT February 2007 — Guts Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Compute the largest positive integer such that is an integer.
    2007 n
解析

英文解析

  1. [ 6 ] Compute the largest positive integer such that is an integer.
    2007 n
    Answer: 9 . Note that 2007 = 3 · 223. Using the fact that the number of times a prime p divides n !2
    is given by
    ⌊ ⌋ ⌊ ⌋ ⌊ ⌋
    n n n + + + · · · ,
    2 3
    p p pit follows that the answer is 9.