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PUMaC 2014 · 数论（A 组） · 第 3 题

PUMaC 2014 — Number Theory (Division A) — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 4 ] Find the number of ending zeros of 2014! in base 9. Give your answer in base 9. x 2
解析
  1. [ 4 ] Find the number of ending zeros of 2014! in base 9. Give your answer in base 9. Solution: 2014 2014 2014 The number of multiples of 3 in 2014! can be calculated as b c + b c + b c + 3 9 27 2014 2014 2014 b c + b c + b c = 1002. Therefore, there should be 501 ending zeros in base 9 for 81 243 729 2014!. Converting to base 9 gives 616 . x 2