**Problem (1)**Prove that there exist infinitely many positive integers such that

**Problem (2)**Prove that there exists only a finite number of positive integers such that

The binomial coefficient is not divisible by prime iff all the base- digits of are smaller than

It has been conjectured that 1, 2, 10, 3159, and 3160 are the only positive numbers for which holds.

## Bibliography

Sequence A030979: Numbers n such that C(2n,n) is not divisible by 3, 5 or 7.

Andrew Granville. "The Arithmetic Properties of Binomial Coefficients."

* indicates original appearance(s) of problem.