For every n,i,j∈ N with 1≤ i<j≤ n/2, does there exist a prime p such that i≤ p and p|gcd!(binom ni,binom nj)?

Erdős Problem #699 — Prime divisors common to two binomial coefficients

For every $n,i,j\in\mathbb N$ with $1\le i<j\le n/2$ , does there exist a prime $p$ such that $i\le p$ and

p\mid\gcd\!\left(\binom ni,\binom nj\right)?

References

Posted 1 month ago · edited 3 weeks ago

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