mersenneforum.org > Math Question on prime powers
 Register FAQ Search Today's Posts Mark Forums Read

 2004-06-27, 21:34 #1 JuanTutors     Mar 2004 3·167 Posts Question on prime powers I'm wondering if it can be shown, or even if it's known yet, whether there exist primes p,q such that (p^m)-(q^n)<=A for an arbitrary positive integer A. I am wondering because, in the special case where p and q are 2 and 3 (or vice versa) it might be easy to prove primality or compositeness of integers N in the range (q^n)
2004-07-04, 12:53   #2
juergen

Mar 2004

29 Posts

Quote:
 Originally Posted by dominicanpapi82 I'm wondering if it can be shown, or even if it's known yet, whether there exist primes p,q such that (p^m)-(q^n)<=A for an arbitrary positive integer A. I am wondering because, in the special case where p and q are 2 and 3 (or vice versa) it might be easy to prove primality or compositeness of integers N in the range (q^n)
Sorry, I don't know the answer to your question, but maybe you would like to read about Catalan's theorem which is the special case A=1.

Catalan's theorem states that there is only one solution (3²-2³) for this equation. It has been prooven a few years ago after about 150 years of uncertainty :o)

Jürgen

 2004-07-07, 07:07 #3 1260   Feb 2003 25 Posts try this page: http://www.primepuzzles.net/conjectures/conj_031.htm

 Similar Threads Thread Thread Starter Forum Replies Last Post mickfrancis Factoring 2 2016-05-06 08:13 plandon Math 7 2009-06-30 21:29 nibble4bits Math 31 2007-12-11 12:56 grandpascorpion Math 49 2007-04-22 17:06 Numbers Puzzles 3 2005-07-13 04:42

All times are UTC. The time now is 08:54.

Thu Dec 3 08:54:15 UTC 2020 up 5:05, 0 users, load averages: 1.90, 1.93, 1.65