Problems

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. ——————————————————————————————————– Proposed by Kenneth Korbin, New York, NY Let N be any positive integer, and let x = N(N + 1). Find the value of Proposed by Neculai Stanciu, “George Emil Palade” Secondary School, Buzău, Romania If a, b, c are consecutive Pythagorean numbers, then solve in the integers the equation: Proposed by Tom Moore, Bridgewater State University, Bridgewater, MA Let Ta and Sb denote the ath triangular and the bth square number, respectively. Find explicit instances of such numbers to prove that every Fibonacci number Fn occurs among the values gcd(Ta, Sb). Proposed by Enkel Hysnelaj, University of Technology, Sydney, Australia and Elton Bojaxhiu, Kriftel, Germany Determine all real valued functions , which satisfy the relation Proposed by José Luis Díaz-Barrero, Polytechnical University of Catalonia, Barcelona, Spain Let a1, a2, … an, (n ≥ 3) be distinct complex numbers. Compute the sum Proposed by Ovidiu Furdui, Technical University of Cluj-Napoca, Cluj-Napoca, Romania Calculate