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