Open Problem Garden - Divisibility of central binomial coefficients - Comments

It seems Problem (1) was (re: Divisibility of central binomial coefficients)

Anonymous — Sun, 29 Jun 2014 11:06:57 +0200

It seems Problem (1) was solved last year, see http://arxiv.org/abs/1010.3070

How about Problem 2?

Ng Yong Hao — Mon, 23 Jul 2012 06:44:51 +0200

It appears that the right reference for question 2 should be A151750 instead.

Anonymous — Wed, 18 Jan 2012 03:25:37 +0100

In the initial comment five values are stated to be not divisible by 3, 5, 7, and 11. That is true for 1 and 3160 but not for 2, 10, and 3159:

The last base-3-digit of 2 is 2. The last base-11-digit of 10 is 10. The last base-5-digit 3159 is 4.

Or check these facts:

2 and 3159 are not in the sequence A030979 (mentioned in the bibliography).

Anonymous — Fri, 27 May 2011 17:00:34 +0200

Does not look like it.

tba — Mon, 14 Mar 2011 20:51:32 +0100

Looks like Problem 1 was solved by http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.3070v1.pdf

maxal — Sun, 05 Aug 2007 05:26:20 +0200

Author(s): Graham

Subject: Number Theory » Combinatorial N.T.

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