Welcome!

PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath's content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members. The entries are contributed under the terms of the Creative Commons By/Share-Alike License in order to preserve the rights of authors, readers and other content creators in a sensible way. We use LaTeX, the lingua franca of the worldwide mathematical community.

Beginning February 23th 2015 we experienced 15 days of downtime when our server stopped working. We moved a backup to DigitalOcean, and we're back online. Some features aren't working yet; we're restoring them ASAP. Please report bugs in the Planetary Bugs Forum or on Github.

Latest Messages

Nov 24

Nov 24
\begin{flushleft} \end{flushleft}

Jun 23
I don't see such a proof. Can you please write it in PlanetMath?

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 23
Pahio, happy to say "Nick" of Mersenneforum.org has given a simple proof.

Jun 22
Before replying to Pahio's call for proof would like to add that I forgot to add the condition: a and p should be co-prime.

Jun 21
Nice theorem! How do you prove it?

Jun 21
Modified Fermat's theorem: Let a belong to the ring of Gaussian integers Then a^(p^2-1)= = 1 (mod p). Here p is a prime number with shape 4m+1 or 4m+3.

Apr 27
Happy to report that "Nick", on mersenneforum.org, has stated that my conjecture can be taken as proved.

Apr 27
Happy to report that "Nick", on mersenneforum.org, has stated that my conjecture can be taken as proved.