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HMMT 二月 2008 · GEN1 赛 · 第 2 题

HMMT February 2008 — GEN1 Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Find the smallest positive integer n such that 107 n has the same last two digits as n .
解析
  1. [ 3 ] Find the smallest positive integer n such that 107 n has the same last two digits as n . Answer: 50 The two numbers have the same last two digits if and only if 100 divides their difference 106 n , which happens if and only if 50 divides n .