Set of 3 Integers each Divisor of Sum of Other Two/Mistake

Source Work

 * The Dictionary
 * $6$
 * $6$


 * The Dictionary
 * $6$
 * $6$

Mistake

 * $1$, $2$, $3$ is also the only set of $3$ integers such that each divides the sum of the other two.

Correction
The statement should be:
 * $1$, $2$, $3$ is also the only coprime set of $3$ distinct integers such that each divides the sum of the other two.

First it is noted that there are two trivial such sets: $\set {1, 1, 1}$ and $\set {1, 1, 2}$.

However, as it specifies set of $3$ integers, and sets by convention contain distinct elements only, the issue is merely one of clarification.

On the other hand, if $\set {a, b ,c}$ is such a set, then $\set {k a, k b, k c}$ is also such a set, which definitely requires the set to be coprime.