3-Smooth Representations of Integers

Abstract

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsRichard BlecksmithRICHARD BLECKSMITH grew up in Cincinnati, Ohio, home of Skyline Chili and the Big Red Machine and now teaches at Northern Illinois University, 50 miles from Chicago style pizza and the Bulls. In between he got a PhD from The University of Arizona, under the direction of John Brillhart. With his wife Sharon, daughter Katie, and various itinerate mathematicians, he lives on a small farm, which five years ago was the site of a big birthday bash for Paul Erdős, who turned 80. He is also a board member of the Malta Band Boosters.Michael McCallumMICHAEL McCALLUM recently took an early retirement from a 25 year career as an electrical engineer at Florida Power & Light Company, where he was mainly involved in systems design and analytical work. He earned his BEE at Georgia Institute of Technology in 1970, his MS in Management Science from the University of Miami (FL), and has done postgraduate work in mathematics at Florida Atlantic University in Boca Raton, Florida. He is author or coauthor of several papers, mainly in power engineering applications. He is a professional engineer in Florida, a senior member of IEEE, and an assistant professor at DeVry Institute of Technology in Decatur, Georgia.J. L. SelfridgeJ. L. SELFRIDGE went to K-12 in Ketchikan, Alaska, and studied math at the University of Washington and at U.C.L.A. with Straus, Motzkin, Swift, and Erdős before Paul was exiled. He has held permanent appointments at IBM Research, University of Washington, Pennsylvania State University, University of Illinois, and Northern Illinois University. Work with Paul Erdős was rekindled in 1966 and continued with many meetings, letters, and joint papers. At a meeting in November, 1995 in North Carolina, Erdős told Selfridge the conjecture with Lewin, and the next morning Selfridge conjectured the best possible form, which is proved by Blecksmith in this paper. McCallum and Selfridge worked on the 2-rep equals 3-rep problem at Florida Atlantic University in Spring 1996. Now in his seventh year of retirement from NIU, he continues to prove, conjecture, and wander about, enjoying life.