HMMT 二月 2003 · GEN1 赛 · 第 8 题
HMMT February 2003 — GEN1 Round — Problem 8
题目详情
英文原题
- A broken calculator has the + and × keys switched. For how many ordered pairs ( a, b )
of integers will it correctly calculate a + b using the labelled + key?
解析
英文解析
- A broken calculator has the + and × keys switched. For how many ordered pairs ( a, b )
of integers will it correctly calculate a + b using the labelled + key?
Solution: 2
b 1
We need a + b = ab , or a = = 1 − , so 1 / ( b − 1) is an integer. Thus b must beb − 1 b − 1
0 or 2, and a is 0 or 2, respectively. So there are 2.