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.

Comments:

Believe it or not, this problem first arose in considering some questions about Tatami tilings.
Appears as problem 11544, in the January 2011 issue of the American Mathematical Monthly, on page 84.
Here is our solution to the problem: solution.

Selected papers that refer to this problem:

Someday there might be some!