HMMT 二月 2000 · GEN 赛 · 第 23 题
HMMT February 2000 — GEN Round — Problem 23
题目详情
- What are the last t w o digits of 7 ?
解析
- Noti e that 7 3 (mo d 4) for k 2 Z ( k is an in teger). 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 eating 77 7 afterw ards. So, learly 7 3 (mo d 4), and sin e the y le has p erio d 4 (mo d 100), 77 7 w e an on lude that 7 43 (mo d 100) .