Triangular Numbers which are Product of 3 Consecutive Integers/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$258,474,216$

Mistake

The largest triangular number to be the product of consecutive integers. The others are $6$, $120$, $210$, $990$ and $185 \, 136$.

This should read:

The largest triangular number to be the product of $3$ consecutive integers. The others are $6$, $120$, $210$, $990$ and $185 \, 136$.

For example, $7140$ is a triangular number which is the product of $2$ (and not $3$) consecutive integers:

$7140 = T_{119} = \dfrac {119 \left({119 + 1}\right)} 2 = 84 \times 85$

Sources

• February 1989: N. Tzanakis and B.M.M. de Weger: On the practical solution of the Thue equation (J. Number Theor. Vol. 31, no. 2: pp. 99 – 132)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $258,474,216$