# Set of 3 Integers each Divisor of Sum of Other Two

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## Theorem

There exists exactly one set of positive integers such that each is a divisor of the sum of the other two:

- $\set {1, 2, 3}$

## Proof

We have that:

- $5 \times 1 = 2 + 3$ so $1 \divides 2 + 3$
- $2 \times 2 = 1 + 3$ so $2 \divides 1 + 3$
- $1 \times 3 = 1 + 2$ so $3 \divides 1 + 2$

It remains to be shown that this is the only such set.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $6$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $6$