Compete · Slovenia
Odbirno tekmovanje (qualifying round) 2025
1Find all pairs of real numbers \(x\) and \(y\) that solve the system \[ \frac{x}{6} + \frac{4}{y} = 2, \qquad \frac{18}{x} + \frac{y}{2} = 5 . \]2Find all three-digit numbers \(\overline{abc}\) that are divisible by \(9\) and satisfy \[ \overline{abc} = a^6 + b^2 + c^3, \] where \(a\), \(b\), \(c\) denote the digits of the number.
Work through the paper in order - each problem opens in the workspace with this paper as its trail.