An optimal lower bound for the Frobenius problem

✍ Scribed by Iskander M. Aliev; Peter M. Gruber

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 127 KB
• Volume: 123
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.05.020

✦ Synopsis

Given N 2 positive integers a 1 , a 2 , . . . , a N with GCD(a 1 , . . . , a N ) = 1, let f N denote the largest natural number which is not a positive integer combination of a 1 , . . . , a N . This paper gives an optimal lower bound for f N in terms of the absolute inhomogeneous minimum of the standard (N -1)-simplex.