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On two conjectures about practical numbers. (English) Zbl 0848.11002
It has been conjectured by {\it M. Margenstern} [J. Number Theory 37, 1-36 (1991; Zbl 0715.11001)] that every positive even integer is a sum of two practical numbers and there are infinitely many triples $m- 2$, $m$, $m+ 2$ of practical numbers. (A number $m$ is practical if every integer in the interval $[1, \sigma(m)]$ is a sum of distinct positive divisors of $m$.) The author establishes these conjectures using a characterization of practical numbers due to {\it B. M. Stewart} [Am. J. Math. 76, 779-785 (1954; Zbl 0056.27004)].

11A25Arithmetic functions, etc.
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