AMM Problem 11544
AMM Problem
Max Alekseyev, Department of Computer Science,
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=m2.
Here, \phi denotes the Euler \phi-function.
Comments:
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Believe it or not, this problem first arose in considering some questions about
Tatami tilings.
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Appears as problem 11544, in the January 2011 issue of the American Mathematical
Monthly, on page 84.
Selected papers that refer to this problem:
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Someday there might be some!