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HMMT 二月 2007 · 冲刺赛 · 第 1 题

HMMT February 2007 — Guts Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 5 ] Define the sequence of positive integers a recursively by a = 7 and a = 7 for all n ≥ 2. n 1 n Determine the last two digits of a . 2007
解析
  1. [ 5 ] Define the sequence of positive integers a recursively by a = 7 and a = 7 for all n ≥ 2. n 1 n Determine the last two digits of a . 2007 4 a a 2005 2005 Answer: 43 . Note that the last two digits of 7 are 01. Also, a = 7 = ( − 1) = − 1 = 3 2006 a 3 2006 (mod 4) since a is odd. Therefore, a = 7 = 7 = 43 (mod 100) . 2005 2007