Compete · Slovenia
Odbirno tekmovanje (qualifying round) 2019
1Show that the number \(7^{2018} + 9^{2020n}\) is divisible by \(5\) for every natural number \(n\).2The real numbers \(a\) and \(b\) satisfy \[ \frac{3a}{a+b} + \frac{2b}{a+2b} = 1 . \] Determine every value that the expression \(\dfrac{2a-3b}{2a+b}\) can take.
Work through the paper in order - each problem opens in the workspace with this paper as its trail.