# Squares equal to Sum of 2 Cubes

## Sequence

The sequence of integers whose square can be expressed as the sum of $2$ coprime cubes begins:

$3, 228, 671, 1261, 6371, 9765, 35 \, 113, 35 \, 928, 40 \, 380, 41 \, 643, 66 \, 599, \ldots$

## Proof

 $\displaystyle 3^2$ $=$ $\displaystyle 9$ $\displaystyle$ $=$ $\displaystyle 8 + 1$ $\displaystyle$ $=$ $\displaystyle 2^3 + 1^3$

 $\displaystyle 228^2$ $=$ $\displaystyle 51 \, 984$ $\displaystyle$ $=$ $\displaystyle 50 \, 653 + 1331$ $\displaystyle$ $=$ $\displaystyle 37^3 + 11^3$

 $\displaystyle 671^2$ $=$ $\displaystyle 450 \, 241$ $\displaystyle$ $=$ $\displaystyle 274 \, 625 + 175 \, 616$ $\displaystyle$ $=$ $\displaystyle 65^3 + 56^3$