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

 2004-06-27, 21:34 #1 JuanTutors     "Juan Tutors" Mar 2004 571 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

111012 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 20:29.

Thu Sep 28 20:29:02 UTC 2023 up 15 days, 18:11, 0 users, load averages: 1.11, 1.12, 1.22