Numbers whose Cube equals Sum of Sequence of that many Squares/Examples/2161

Example of Number whose Cube equals Sum of Sequence of that many Squares

 * $\displaystyle 2161^3 = \sum_{k \mathop = 1}^{2161} \left({988 + k}\right)^2$

Proof
From Numbers whose Cube equals Sum of Sequence of that many Squares:
 * $\displaystyle m^3 = \sum_{k \mathop = 1}^m \left({n + k}\right)^2$

for $m = 2161$ and for $n$ given by:


 * $n = \dfrac {m + 1} 2 \pm \dfrac 1 6 \sqrt {33 m^2 + 3}$

So in this instance:

This gives:
 * $n = 988, n = -3150$

which leads to the two solutions: