MathDB

IMO ShortList 2002, number theory problem 3

Source: IMO ShortList 2002, number theory problem 3

September 28, 2004

algebranumber theoryprimesDivisorsIMO Shortlist

Problem Statement

Let

p_1,p_2,\ldots,p_n

be distinct primes greater than

3

. Show that

2^{p_1p_2\cdots p_n}+1

has at least

4^n

divisors.