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PUMaC 2015 · 数论（B 组） · 第 2 题

PUMaC 2015 — Number Theory (Division B) — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 3 ] What is the 22nd positive integer n such that 22 ends in a 2? (when written in base 10). 2
解析
  1. [ 3 ] What is the 22nd positive integer n such that 22 ends in a 2? (when written in base 10). Solution: The last digits of the powers of 22 cycle 2 , 4 , 8 , 6 , 2 , 4 , 8 , 6 , . . . . The answer is thus the 22nd term of the arithmetic sequence 1 , 5 , 9 , . . . , which is 85 . Author: Eric Neyman 2