HMMT 二月 2002 · 冲刺赛 · 第 19 题
HMMT February 2002 — Guts Round — Problem 19
题目详情
英文原题
- [8] For how many integers a (1 ≤ a ≤ 200) is the number a a square?
解析
英文解析
- 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 , whichis 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.