Abstract :
A positive integermis said to be a practical number if every integern, with 1less-than-or-equals, slantnless-than-or-equals, slantσ(m), is a sum of distinct positive divisors ofm. 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 numbersmsuch thatm−2 andm+2 are also practical.
