Tag Archives: fixed

2012-8 Non-fixed points

Let X be a finite non-empty set. Suppose that there is a function \(f:X\to X\) such that \( f^{20120407}(x)=x\) for all \(x\in X\). Prove that the number of elements x in X such that \(f(x)\neq x\) is divisible by 20120407.

GD Star Rating
loading...