AMM Problem 11544

AMM Problem

Max Alekseyev, Department of Computer Science and Engineering, University of South Carolina.
Frank Ruskey, Department of Computer Science, University of Victoria.

Abstract:

Prove that if m is a positive integer, then

$\sum_{k=0}^{m-1}\phi(2k+1)\left\lfloor\frac{m+k}{2k+1}\right\rfloor =m^2.$

Here, $\phi$ denotes the Euler $\phi$-function.