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.
* indicates original appearance(s) of problem.