On two conjectures about practical numbers (Q1907859)

It has been conjectured by \textit{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 \textit{B. M. Stewart} [Am. J. Math. 76, 779-785 (1954; Zbl 0056.27004)].