# Smallest Triplet of Consecutive Integers Divisible by Cube

## Theorem

The smallest sequence of triplets of consecutive integers each of which is divisible by a cube greater than $1$ is:

$\tuple {1375, 1376, 1377}$

## Proof

 $\displaystyle 1375$ $=$ $\displaystyle 11 \times 5^3$ $\displaystyle 1376$ $=$ $\displaystyle 172 \times 2^3$ $\displaystyle 1377$ $=$ $\displaystyle 51 \times 3^3$

## Historical Note

This result is reported by David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$ as appearing in Eureka in $1982$, but it has been impossible to corroborate this.