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On Sets of Natural Numbers Whose Sumset is Free of Squares

✍ Scribed by Tomasz Schoen

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 78 KB
Volume: 88
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.2985

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✦ Synopsis

Let A be a set of natural numbers such that the set A+A contains no perfect squares. We prove that if the density d(A) exists, it is not larger than 2Â5.

1999 Academic Press

In this note we are concerned with a problem of Erdo s and Silverman (see ) who asked about the maximal density d max of a set A N such that for every a, b # A the sum a+b is never a square of an integer. Massias observed that if

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