HMMT 十一月 2015 · 冲刺赛 · 第 8 题
HMMT November 2015 — Guts Round — Problem 8
题目详情
- [ 7 ] For how many pairs of nonzero integers ( c, d ) with − 2015 ≤ c, d ≤ 2015 do the equations cx = d and dx = c both have an integer solution?
解析
- [ 7 ] For how many pairs of nonzero integers ( c, d ) with − 2015 ≤ c, d ≤ 2015 do the equations cx = d and dx = c both have an integer solution? Proposed by: Yang Liu Answer: 8060 We need both c/d and d/c to be integers, which is equivalent to | c | = | d | , or d = ± c . So there are 4030 ways to pick c and 2 ways to pick d , for a total of 8060 pairs.