17th Eötvös Competition Problems 1910

1.  α, β, γ are real and satisfy α2 + β2 + γ2 = 1. Show that -1/2 ≤ αβ + βγ + γα ≤ 1. 2.  If ac, bc + ad, bd = 0 (mod n) show that bc, ad = 0 (mod n). 3.  ABC is a triangle with angle C = 120o. Find the