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On Two Conjectures about Practical Numbers

✍ Scribed by Giuseppe Melfi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 240 KB
Volume: 56
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0012

No coin nor oath required. For personal study only.

✦ Synopsis

A positive integer m is said to be a practical number if every integer n, with 1 n _(m), is a sum of distinct positive divisors of m. In this note we prove two conjectures of Margenstern:

(i) every even positive integer is a sum of two practical numbers;

(ii) there exist infinitely many practical numbers m such that m&2 and m+2 are also practical.

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