Compete · Slovenia
Odbirno tekmovanje (qualifying round) 2018
1Find all real numbers \(x\) that satisfy the inequality \[ \frac{|x-3| + x}{x+1} < 1 . \]2Show that the number \[ 2^{\,2n+3} + 3^{\,n+2}\cdot 7^{\,n} \] is divisible by \(17\) for every natural number \(n\).
Work through the paper in order - each problem opens in the workspace with this paper as its trail.