# Smallest Quadruplet of Consecutive Integers Divisible by Cube

## Theorem

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

$\tuple {22 \, 624, 22 \, 625, 22 \, 626, 22 \, 627}$

## Proof

 $\displaystyle 22 \, 624$ $=$ $\displaystyle 2828 \times 2^3$ $\displaystyle 22 \, 625$ $=$ $\displaystyle 181 \times 5^3$ $\displaystyle 22 \, 626$ $=$ $\displaystyle 838 \times 3^3$ $\displaystyle 22 \, 627$ $=$ $\displaystyle 17 \times 11^3$

## Historical Note

This result is reported by David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$ as the work of Stephane Vandemergel, but details are lacking.