16th Eötvös Competition Problems 1909

1.  Prove that (n + 1)3 ≠ n3 + (n - 1)3 for any positive integer n. 2.  α is acute. Show that α < (sin α + tan α)/2. 3.  ABC is a triangle. The feet of the altitudes from A, B, C are P, Q, R respectively, and P,