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planetmath.org

Math for the people, by the people.

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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.

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Latest Messages  

[P] Pointless by jeremyboden Apr 15
a/0 is the same thing as a/1 I advise you to give up this division by zero idea.

[p] figures by pahio Apr 15
Dear unlord, It's nice to hear that there exists a solution to that character problem. Of course there are here other, bigger problems -- one of the hardest ones is perhaps formed by the figures (graphs etc.) in the PlanetMath articles.

re: special math characters by unlord Apr 12
OK, this is not good news, but at least there is a fix. The problem has to do with the special database encoding that is needed to make these special characters work. It was set up correctly on the old server, and for some reason I thought, or rather imagined, that it would work well on the new server. More work will have to be done to fix it. However, having done it once -- in the distant past -- I can figure out how to do it again. Thanks for letting me know.>

special math characters by pahio Apr 2
Hi admins, the math fraktur letters \mathfrak{ } and the math calligraphy letters \mathcal{ } are not visible in the entries -- one sees them only as question marks (see e.g. the entry "algebraic number theory"). In the entry "ideal multiplication laws" you see much such question marks!>

[p] SEARCH MACHINE by pahio Feb 20
Hi admins, the search machine does not work. Please start it again!

[P] A bit of history by akdevaraj Feb 20
Before giving further comments on Fermat's theorem and related matters let me give a bit of history: 1640 Fermat's theorem 1740(circa) Euler's generalisation of FT 2004 Euler's generalisation of FT - a further generalisation (Devaraj)) 2006 Minimum Universal exponent generalisation of Fermat's T. (Devaraj). 2012 Ultimate generalisation of FT -Pahio and Devaraj My paper " Euler's generalisation......." freed FT of the requirement of base and exponent to be coprime. Secondly we can identify small factors of very large numbers by merely operating on the exponents. Before concluding this message I would like to thank Pahio for enabling ├╝ltimate generalisation of FT.

[P] Euler's generalisation of Fermat's theorem in k(i) (contd) by akdevaraj Feb 19
Before generalising let me give another related example: ((15 + 7*I)^12-1)/21 also yields a Gaussian integer as quotient.

[P] Euler's generalisation of Fermat's theorem in k(i) by akdevaraj Feb 18
I will just give an example to illustrate: ((21+i)^12-1)/21 is a Gaussian integer. Needless to say we can verify this only if we have pari or similar software.

General Method for Summing Divergent Series by Sinisa Feb 17
I discovered general method for summing divergent series, which we can also consider as a method for computing limits of divergent sequences and functions in divergent points, In this case, limits of sequences of their partial sums. I applied the method to compute the value of some divergent integrals. https://m4t3m4t1k4.wordpress.com/2015/02/14/general-method-for-summing-divergent-series-determination-of-limits-of-divergent-sequences-and-functions-in-singular-points-v2/>

[p] Hi Edwards, I don't know if by dh2718 Feb 14
Hi Edwards, I don't know if this is still actual, but here is a simple way to prove it. Start writing down the (square of) the distance of two any points in the plane, as a function of their 4 coordinates. There are four constraints on these points. They both have to be on a given ellipse and they both have to be on a straight line of given inclination m. Now use Lagrange multipliers to maximize the distance as a function of the coordinates and the position of the line (given, for example, by its crossing point with the x axis). The rest is straightforward.

[P] A puzzle by akdevaraj Feb 3
Fermat's theorem works in terms of square matrices; however Euler's generalisation of Fermat's theorem in terms of matrices does not seem to be true.

[P] A request to Dr. Puzio by akdevaraj Jan 30
I use pari software and sometimes I would like to display the calculations/programs on the space for messages; however, I am unable to paste them. Would be glad if this and adding files are enabled.

[P] Fermat's theorem in terms of matrices. by akdevaraj Jan 29
Let X be a square matrix in which each element is an odd prime. Then (a^(X-I)-I)/X yields a square matrix in which the elements belong to Z. Here a is co-prime with each element of X. Also I is the identity matrix.

[P] pseudoprimes in k(i) (contd)- a small by-product by akdevaraj Jan 28
A small by-product of research in area of pseudoprimes in k(i): Take a product of two numbers each with shape 4m+3. Let x be this composite number. x is pseudo to base (x-1).Examples 21, 33, 57 etc. (20^20-1)/21 yields a rational integer.