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PUMaC 2013 · 数论（B 组） · 第 4 题

PUMaC 2013 — Number Theory (Division B) — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 4 ] Compute the smallest integer n ≥ 4 such that ends in 4 or more zeroes (i.e. the 4 ( ) n rightmost four digits of are 0000). 4
解析
  1. [ 4 ] Compute the smallest integer n ≥ 4 such that ends in 4 or more zeroes (i.e. the 4 ( ) n rightmost four digits of are 0000). 4 ( ) n 4 7 Solution Firstly, 2 | iff 2 | n ( n − 1)( n − 2)( n − 3) if and only if n ≡ 0 , 1 , 2 , 3 (mod 64). 4 ( ) n 4 Next, 5 | if and only if n ≡ 0 , 1 , 2 , 3 (mod 625). By trial, the smallest n is 8128. 4