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HMMT 二月 2007 · 冲刺赛 · 第 1 题

HMMT February 2007 — Guts Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  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

英文解析

  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