Sum of 4 Consecutive Binomial Coefficients forming Square/Mistake

Source Work

 * The Dictionary
 * $767$
 * $767$

Mistake
Mistake $1$:
 * $\dbinom {767} 1 + \dbinom {767} 2 + \dbinom {767} 3 + \dbinom {767} 4$ is a perfect square, $8672^2$.

Mistake $2$:
 * The smaller solutions are $7$, $15$ and $74$.

The first mistake is that it is $\dbinom {767} 0 + \dbinom {767} 1 + \dbinom {767} 2 + \dbinom {767} 3 = 8672^2$.

The second mistake is that the numbers $-1$, $0$ and $2$ have the same property.

is perhaps excused the first two, as they may not have been in his purview, but omitting $2$ is a less forgivable oversight, considering the complete set is given in, which he himself references.