PUMaC 2016 · 代数（B 组） · 第 4 题
PUMaC 2016 — Algebra (Division B) — Problem 4
题目详情
- Let f ( x ) = 15 x − 2016. If f ( f ( f ( f ( f ( x ))))) = f ( x ), find the sum of all possible values of x . log y 2
解析
- Note that f ( f ( f ( f ( f ( x ))))) = f ( x ) is a linear equation in x and thus has one solution. If f ( x ) = x then clearly this equation is satisfied. Thus the solution is the solution to the equation x = 15 x − 2016, which is 144 . Problem written by Eric Neyman.