4

Part of 2008 Regional Competition For Advanced Students

Problems(1)

39th Austrian Mathematical Olympiad 2008

Source: round1, problem4

For every positive integer

n

let a_n\equal{}\sum_{k\equal{}n}^{2n}\frac{(2k\plus{}1)^n}{k} Show that there exists no

n

a_n

is a non-negative integer.

floor functionlogarithmsmodular arithmeticnumber theory unsolvednumber theory