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HMMT 十一月 2011 · GEN 赛 · 第 4 题

HMMT November 2011 — GEN Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 4 ] Determine the remainder when
    1 · 2 2 · 3 2011 · 2012
    2 2 2
    2 + 2 + · · · + 2
    is divided by 7.
解析

英文解析

  1. [ 4 ] Determine the remainder when
    1 · 2 2 · 3 2011 · 2012
    2 2 2
    2 + 2 + · · · + 2
    is divided by 7.
    Answer: 1 We have that 2 ≡ 1 (mod 7). Hence, it suffices to consider the exponents modulo 3