HMMT 二月 2003 · GEN1 赛 · 第 8 题
HMMT February 2003 — GEN1 Round — Problem 8
题目详情
- 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
- 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 be b − 1 b − 1 0 or 2, and a is 0 or 2, respectively. So there are 2.