返回题库

HMMT 二月 2000 · GEN 赛 · 第 23 题

HMMT February 2000 — GEN Round — Problem 23

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. What are the last t w o digits of 7 ?
解析

英文解析

  1. Noti e that 7 3 (mo d 4) for k 2 Z ( k is an integer). Also, 7 7 (mo d 100),
    2 3 4
    7 49 (mo d 100), 7 43 (mo d 100), 7 1 (mo d 100), with the y le rep eatingafterw ards. So, learly 7 3 (mo d 4), and sin e the y le has p erio d 4 (mo d 100),777
    we an on lude that 7 43 (mo d 100) .777