1st Eötvös Competition Problems 1894

1.  Show that { (m, n): 17 divides 2m + 3n} = { (m, n): 17 divides 9m + 5n}. 2.  Given a circle C, and two points A, B inside it, construct a right-angled triangle PQR with vertices on C and hypoteneuse QR such that A lies on the side PQ and B lies on the side PR. For which A, B is this not possible?