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HMMT 二月 2002 · 冲刺赛 · 第 19 题

HMMT February 2002 — Guts Round — Problem 19

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [8] For how many integers a (1 ≤ a ≤ 200) is the number a a square?
解析
  1. For how many integers a (1 ≤ a ≤ 200) is the number a a square? a a/ 2 2 a ( a − 1) / 2 2 Solution: 107 If a is even, we have a = ( a ) . If a is odd, a = ( a ) · a , which is a square precisely when a is. Thus we have 100 even values of a and 7 odd square values 2 2 2 (1 , 3 , . . . , 13 ) for a total of 107.