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The least common multiple of random sets of positive integers

✍ Scribed by Cilleruelo, Javier; Rué, Juanjo; Šarka, Paulius; Zumalacárregui, Ana

Book ID
124103935
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
233 KB
Volume
144
Category
Article
ISSN
0022-314X

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We present here a method which allows to derive a nontrivial lower bounds for the least common multiple of some finite sequences of integers. We obtain efficient lower bounds (which in a way are optimal) for the arithmetic progressions and lower bounds less efficient (but nontrivial) for quadratic s

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Let n be a positive integer. Let S = {x 1 , . . . , x n } be a set of n distinct positive integers. The least common multiple (LCM) matrix on S, denoted by [S], is defined to be the n × n matrix whose (i, j )-entry is the least common multiple [x i , x j ] of x i and x j . The set S is said to be gc