National and Regional Contests Bosnia Herzegovina Contests Bosnia Herzegovina Team Selection Test 2009 Bosnia Herzegovina Team Selection Test 3 Bosnia 2009 Problem 6 Problem Statement Let n n n x x x x , 2 x , … , n x x,2x,\dots,nx x , 2 x , … , n x 1 x , 2 x , … , ⌊ n x ⌋ x \frac{1}{x},\frac{2}{x},\dots,\frac{\left\lfloor nx\right\rfloor }{x} x 1 , x 2 , … , x ⌊ n x ⌋ ⌊ x ⌋ + ⌊ 2 x ⌋ + ⋯ + ⌊ n x ⌋ + ⌊ 1 x ⌋ + ⌊ 2 x ⌋ + ⋯ + ⌊ ⌊ n x ⌋ x ⌋ = n ⌊ n x ⌋
\left\lfloor x\right\rfloor +\left\lfloor 2x\right\rfloor +\dots+\left\lfloor nx\right\rfloor +\left\lfloor \frac{1}{x}\right\rfloor +\left\lfloor \frac{2}{x}\right\rfloor +\dots+\left\lfloor \frac{\left\lfloor nx\right\rfloor }{x}\right\rfloor =n\left\lfloor nx\right\rfloor ⌊ x ⌋ + ⌊ 2 x ⌋ + ⋯ + ⌊ n x ⌋ + ⌊ x 1 ⌋ + ⌊ x 2 ⌋ + ⋯ + ⌊ x ⌊ n x ⌋ ⌋ = n ⌊ n x ⌋