Problem A. 787. (November 2020)

A. 787. Let $\displaystyle p_n$ denote the $\displaystyle n^{\text{th}}$ prime number and define $\displaystyle a_n=\lfloor p_n \nu \rfloor$, where $\displaystyle \nu$ is a positive irrational number. Is it possible that there exist only finitely many $\displaystyle k$ such that $\displaystyle \binom{2a_k}{a_k}$ is divisible by $\displaystyle p_i^{10}$ for all $\displaystyle i=1,2,\ldots, 2020$?

Submitted by: Abhishek Jha, Delhi, India and Ayan Nath, Tezpur, India

(7 pont)

Deadline expired on December 10, 2020.

Statistics:

3 students sent a solution.
7 points:	Fleiner Zsigmond, Füredi Erik Benjámin.
0 point:	1 student.

Problems in Mathematics of KöMaL, November 2020