Problems Section

Abstract

This section of the Journal offers readers an opportunity to exchange interesting mathematical problems and solutions. Please send them to Ted Eisenberg, Department of Mathematics, Ben-Gurion University, Beer-Sheva, Israel or fax to: 972-86-477-648. Questions concerning proposals and/or solutions can be sent via e-mail to eisenbt@013.net. Solutions to previously stated problems can be seen at http://www.ssma.org/publications. ———————————————————————————— 5295: Proposed by Kenneth Korbin, New York, NY A convex cyclic hexagon has sides 5296: Proposed by Roger Izard, Dallas, TX Consider the “Star of David,” a six-pointed star made by overlapping the triangles ABC and FDE. Let Prove that r + p = (3pr + 1)/2. 5297: Proposed by Tom Moore, Bridgewater State University, Bridgewater, MA Let sn = n2, tn = n (n + 1)/2, and pn = n (3n − 1)/2, for positive integers n, be the square, triangular, and pentagonal numbers, respectively. Prove, independently of each other, that ta + pb = tc, ta + sb = pc, pa + sb = sc 5298: Proposed by D. M. Bătinetu-Giurgiu, Matei Basarab National College, Bucharest, Romania and Neculai Stanciu, George Emil Palade Secondary School, Buzău, Romania Let (an)n ≥ 1 be an arithmetic progression and m a positive integer. Calculate 5299: Proposed by José Luis Díaz-Barrero, Barcelona Tech, Barcelona, Spain Without the aid of a computer, show that 5300: Proposed by Ovidiu Furdui, Technical University of Cluj-Napoca, Cluj-Napoca, Romania Let n ≥ 1 be an integer. Prove that