Fork me on GitHub

planetmath.org

Math for the people, by the people.

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.

User login

Error message

Notice: Undefined index: id in planetmath_legacy_urls_init() (line 5 of /home/jcorneli/beta/sites/all/modules/planetmath_legacy_urls/planetmath_legacy_urls.module).


Latest Messages  

[P] isolated square free numbers by akdevaraj 10:39 am
I prefer the definition as follows: prime numbers and composite numbers in which each prime factor occurs only with exponent equal to one. Examples of such composites: 6, 35, 65, 93....

[P] isolated square free numbers by akdevaraj 10:39 am
I prefer the definition as follows: prime numbers and composite numbers in which each prime factor occurs only with exponent equal to one. Examples of such composites: 6, 35, 65, 93....

[P] I forgot the number 19. by perucho Feb 20
So that, the first twin isolated square-free numbers are $ {17,19}$, sorry.

[p] Euler's generalisation of Fermat's theorem ....... by akdevaraj Feb 17
This works even when the base is a Gaussian integer: Reading GPRC: gprc.txt ...Done. GP/PARI CALCULATOR Version 2.6.1 (alpha) i686 running mingw (ix86/GMP-5.0.1 kernel) 32-bit version compiled: Sep 20 2013, gcc version 4.6.3 (GCC) (readline v6.2 enabled, extended help enabled) Copyright (C) 2000-2013 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 4000000, primelimit = 500000 (17:50) gp > ((14+15*I)^104-1)/105 = -249662525598174865517621222098021785366399633335910441957688800663877876192221716937263714468906280908614454012799368615180549371243472 - 118511838209654103558982122027130965758920275429164915998560474682902951765213030198935065103035392002339412087987613469408163154998032*I (17:51) gp >

[p] Euler's generalisation of Fermat's theorem ....... by akdevaraj Feb 17
This works even when the base is a Gaussian integer: Reading GPRC: gprc.txt ...Done. GP/PARI CALCULATOR Version 2.6.1 (alpha) i686 running mingw (ix86/GMP-5.0.1 kernel) 32-bit version compiled: Sep 20 2013, gcc version 4.6.3 (GCC) (readline v6.2 enabled, extended help enabled) Copyright (C) 2000-2013 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 4000000, primelimit = 500000 (17:50) gp > ((14+15*I)^104-1)/105 %1 = -249662525598174865517621222098021785366399633335910441957688800663877876192221716937263714468906280908614454012799368615180549371243472 - 118511838209654103558982122027130965758920275429164915998560474682902951765213030198935065103035392002339412087987613469408163154998032*I (17:51) gp >

[p] Fermat's theorem by akdevaraj Jan 27
Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1 and b) the exponent and base are co-prime. ((2+3*I)^16-1)/17 = -47977440 - 803040*I

[p] Fermat's theorem by akdevaraj Jan 27
Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1 and b) the exponent and base are co-prime. ((2+3*I)^16-1)/17 %1 = -47977440 - 803040*I

[p] Fermat's theorem by akdevaraj Jan 27
Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1 and b) the exponent and base are co-prime. ((2+3*I)^16-1)/17 %1 = -47977440 - 803040*I

[p] An open invitation by akdevaraj Jan 26
Join maths corner on facebook. Procedure: join fb and I can add you as member - your contributions are welcome.

[p] Happy by akdevaraj Jan 26
Happy to see Pahio is again active on this site!

[p] Happy by akdevaraj Jan 26
Happy to see Pahio is again active on this site!

[p] Happy by akdevaraj Jan 26
Happy to see Pahio is again active on this site!

[p] Happy by akdevaraj Jan 26
Happy to see Pahio is again active on this site!

[p] 1 11 111 1111… by phongphanp Jan 5
1 11 111 1111... This could be an example to here, the normal.