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. ————————————————————– Given triangle ABC with integer length sides and integer area. The vertices have coordinates A(0, 0), B(x, y), and C(z, w) with x 2 + y 2 − z 2 + w 2 = 1 . Find positive integers x, y, z, and w if the perimeter is 84. Let abcd be a four-digit number in base 10, none of which are zero, such that the last four digits in the square of abcd are abcd, the number itself. Find the number abcd. Let a convex quadrilateral ABCD have area S and side lengths A B ¯ = a , B C ¯ = b , C D ¯ = c , D A ¯ = d and area S. Show that Let f(x) and g(x) be arbitrary functions defined for all x ∈ ℛ. Prove that there is a function h(x) such that is an odd function for all x ∈ ℛ. Let a1, a2, … , an be positive real numbers with n ≥ 4. Prove that Let k ≥ 2 be an integer. Calculate Calculate