7

Part of 2009 China Northern MO

Problems(1)

xy=1 and y irrational >1 if [x [ny] ] =n-1 ,

Source: China Northern MO 2009 p7 CNMO

\lfloor m \rfloor

be the largest integer smaller than

m

x,y \in \mathbb{R+}

, For all positive integer

n

\lfloor x \lfloor ny \rfloor \rfloor =n-1

xy=1

y

is an irrational number larger than

1

number theoryalgebrafloor function