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HMMT 二月 2013 · 冲刺赛 · 第 11 题

HMMT February 2013 — Guts Round — Problem 11

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 prime factorization of 1007021035035021007001 . (You should write your answer in thee e e
    1 2 kform p p . . . p , where p , . . . , p are distinct prime numbers and e , . . . , e are positive integers.)
    1 k 1 k
    1 2
    kk
解析

英文解析

  1. [ 6 ] Compute the prime factorization of 1007021035035021007001 . (You should write your answer in thee e e
    1 2 kform p p . . . p , where p , . . . , p are distinct prime numbers and e , . . . , e are positive integers.)
    1 k 1 k
    1 2
    7 7 7 k
    Answer: 7 · 11 · 13 The number in question is
    ( )
    ∑7
    i 7 7 7 7 77
    1000 = (1000 + 1) = 1001 = 7 · 11 · 13 .
    i =0 ik