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PUMaC 2014 · 团队赛 · 第 3 题

PUMaC 2014 — Team Round — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 4 ] How many integer x are there such that is a positive integer? x 6
解析
  1. [ 4 ] How many integer x are there such that is a positive integer? x − 6 Solution: 2 x − 6 30 We see that = x + 6 + . Since there are 8 diviors of 30, we see that taking x − 6 x − 6 the divisors and adding 6 will be all the solutions for x > 6. For x < 6, the denominator is negative, hence we see that the numerator needs to be negative as well. Thus we check x = 2 , 1 , 0 , − 1 , − 2, and we see that x = 1 , 0 are two additional solutions, giving us a total of 8 solutions.