Numbers with Square-Free Binomial Coefficients/Mistake

Source Work

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

The Dictionary

$23$

Mistake

For every $n$ greater than $23$, none of the binomial coefficients $\dbinom n k$ are square-free.

Correction

Take $\dbinom {26} 1 = 26$ for example, which is indeed square-free.

What appears to be meant is:

For every $n$ greater than $23$, there exists a binomial coefficient $\dbinom n k$ that is not square-free.

As is seen in Numbers with Square-Free Binomial Coefficients, the list of numbers $n$ such that $\dbinom n k$ are squarefree for all $k = 0, \dots, n$ is given by:

$1, 2, 3, 5, 7, 11, 23$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $23$