Extremal theorems on divisors of a number

✍ Scribed by Shuo-Yen Robert Li

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 884 KB
• Volume: 24
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90171-1

✦ Synopsis

For e-.ery positive integer IV, we determine the rnaxintum sizes of collections C and C' of divisors of N subject to the following restrictions. 1' any IWO numbers in C are coprime. then their least common multiple must he N. If any k nu nbers (k arbitrary) in C' have the greatest common divisor 1. then their least common multiplr must be IV. For the special case that N is <qbare fret-. the maximum sizes of C and C' have previously been determined. Since ever! number can be thought of as a multiset of primes, tt IS work can he regarded a\ 311 extension of theorems on families of finite sets to families of mllltisets.