For fixed r≥0, does the set of integers n for which binom nk is squarefree for at least r indices 1≤ k<n have a natural density, and is that density positive?

Erdős Problem #378 — Squarefree entries in rows of Pascal's triangle

About 46 years old · traced to 1980

For fixed $r\geq0$ , does the set of integers $n$ for which $\binom nk$ is squarefree for at least $r$ indices $1\leq k<n$ have a natural density, and is that density positive?

References

Primary source

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

binomial-coefficients number-theory

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