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HMMT 二月 2013 · 冲刺赛 · 第 11 题

HMMT February 2013 — Guts Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

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