Compete · Slovenia
Odbirno tekmovanje (qualifying round) 2024
1Find all pairs of integers \(a\) and \(b\) satisfying \[ 4a - 2b + 22ab^2 - 11b^3 = 2024 . \]2A rectangle \(ABCD\) satisfies \(|AB| = 10\) and \(|AC| = 5\sqrt{7}\). Let \(M\) be the midpoint of the side \(AB\). Inside the rectangle we draw the semicircle with diameter \(AB\) and the triangle \(CDM\), …
Work through the paper in order - each problem opens in the workspace with this paper as its trail.