39th Austrian Mathematical Olympiad 2008
Source: round1, problem4
February 10, 2009
floor functionlogarithmsmodular arithmeticnumber theory unsolvednumber theory
Problem Statement
For every positive integer let
a_n\equal{}\sum_{k\equal{}n}^{2n}\frac{(2k\plus{}1)^n}{k}
Show that there exists no , for which is a non-negative integer.