Set of 3 Integers each Divisor of Sum of Other Two/Mistake
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Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $6$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $6$
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.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$