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can t understand what you are trying to do Greetings p Approximate values of real by RKJCHENNAI Feb 11 http rkmath yolasite com resources Roots 20sum 20and 20multiplication pdf Finding approximate values of real roots equation by RKJCHENNAI Feb 11 p search engine by akdevaraj Feb 4 Search engine still not functioning p Legendre s symbol by akdevaraj Jan 29 a p is the Legendre symbol for quadratic residues and non residues If a p 1 it means a is not a quadratic residue of p Another way of expressing this the p under ref is an impossible prime factor of x 2 a For further examples of this concept see A123239 A 072936 and A 119691 on OEIS p Book by akdevaraj Jan 26 Currently reading prime numbers a computational perspective by Richard Crandall and Carl Pomerance This is a monumental book on prime numbers primality testing and factorisation p Book by akdevaraj Jan 26 Currently reading prime numbers a computational perspective by Richard Crandall and Carl Pomerance This is a monumental book on prime numbers primality testing and factorisation p Book by akdevaraj Jan 26 Currently reading prime numbers a computational perspective by Richard Crandall and Carl Pomerance This is a monumental book on prime numbers primality testing and factorisation p Indirect primality testing by akdevaraj Jan 24 Dear dh2718 thanks for the compliment p Indirect primality testing by akdevaraj Jan 23 Dear Permalink you are right about bio age I am 85 p Indirect primality testing by akdevaraj Jan 13 Dear Peruchio f x k f x star means multiply k belongs to Z Thus in this case since f x x 2 x 1 f x k f x means 1 3k Trust this is clear more Latest Messages p Another good book by akdevaraj Mar 27 Prime obsession by John Derbyshire it is on Riemann Hypothesis extremely readable pstricks by Wkbj79 Mar 15 p Deleting by akdevaraj Feb 15 How do we delete a message I clicked on edit then tried to delete but did not succeed p Indirect primality testing by perucho Feb 15 Thanks akdevaraj for clarify what means k confused me since here in PM one simply writes f x kf x Your example is quite complex so f x kf x is too long But let s suppose f x x 2 so f x kf x f x kx 2 x kx 2 2 k 2x 4 2kx 3 x 2 Let s prove a couple of examples If k 0 f x 0f x 0 2x 4 2 0 x 3 x 2 x 2 f x as it should be If k 1 f x 1f x 1 2x 4 2 1 x 3 x 2 x 2 2x 3 x 4 x x 2 2 f x x 2 again as it should be Thus I can t understand what you are trying to do Greetings p Approximate values of real by RKJCHENNAI Feb 11 http rkmath

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Open archived version from archive - The PlanetMath FAQ | planetmath.org

t been attempted in a while You can still find copies of the Free Encyclopedia of Mathematics online however and new versions will be created when we have time 1 6 Do I need to know TeX LaTeX to write a PlanetMath entry It s strongly recommended However LaTeX is not hard to learn and we have provided an easy way to view the source code of any existing PlanetMath entry to faciliate learning how to write mathematics in TeX A PlanetMath specific LaTeX guide can can be found as a Site Doc There are also quite a few good online references and tutorials for TeX and LaTeX Getting Started With LaTeX Hypertext Help with LaTeX The Harvard Guide to TeX A Guide to LaTeX The Not So Short Introduction to LaTeX2e 1 7 Who can contribute Anyone can make an account and immediately start creating entries Of course if you can t take constructive criticism you might want to reconsider 1 8 Who reviews content and how Anyone who wants to The chief means of peer review is via the corrections system Anyone can submit corrections of type addendum or erratum to any entry Points are given for accepted corrections providing a means of crediting the reviewing party s contribution It is up to the author to determine of a correction is worth accepting However corrections are always available for viewing If a correction is either wrongly accepted or rejected others may notice this and file further corrections 1 9 Who owns contributed material The authors of content retain all rights they posses by law By joining PlanetMath they also agree to license to PlanetMath all content they submit to the site Under this arrangement authorship recognition must be preserved but aside from that anybody can make digital copies print versions or hard copy duplicates Anybody can set up their own web site with content from PlanetMath Anybody can sell compilations of that content For more details see the Creative Commons Attribution ShareAlike license 1 10 How can I help the project financially or otherwise Please see our page on supporting PlanetMath 2 Usage Questions 2 1 How can I contribute 1 Make an account 2 Browse around get a feel for the site 3 Read the New User documentation 4 Log in click on Encyclopedia under add in your user box 5 Write your entry Have a LaTeX guide handy if you don t already know LaTeX 6 Preview submit 2 2 How do I know what content has already been added You don t really need to other than to avoid directly duplicating a concept someone else has already written an entry for However this can be avoided by simply using the search engine In addition the system will provide a warning at entry adding time if the title of your entry is suspiciously similar to the title of an existing entry Aside from this many people are worried about how they can possibly hyperlink their entries

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Open archived version from archive - Planetary Bugs | planetmath.org

1 By unlord 2 years 6 months ago Normal topic Delete a collection By Aleph Zero 2 years 8 months ago 3 By pahio 2 years 8 months ago Normal topic search feature broken in new planetmath and now in noosphere By remag12 2 years 10 months ago 1 By unlord 2 years 10 months ago Normal topic Scores Not Incrementing By Jon Awbrey 2 years 10 months ago 2 By Jon Awbrey 2 years 10 months ago Normal topic local articles By Aleph Zero 2 years 11 months ago 1 By Aleph Zero 2 years 11 months ago Normal topic Enhancement By Aleph Zero 2 years 11 months ago 1 By unlord 2 years 11 months ago Normal topic Links in PlanetMath FAQ By Aleph Zero 2 years 11 months ago 3 By unlord 2 years 11 months ago Normal topic Repeated bug report By porton 3 years 3 weeks ago 4 By unlord 3 years 3 days ago Normal topic The font is too small By porton 3 years 1 month ago 7 By porton 3 years 1 month ago Normal topic An error in Latest Messages dates By porton 3 years 1 month ago 0 n a Normal topic Versions links do not work By porton 3 years 1 month ago 1 By unlord 3 years 1 month ago Normal topic Hyperlinking and child articles do not work By porton 3 years 1 month ago 2 By porton 3 years 1 month ago Normal topic RSS feed does not work anymore By porton 3 years 1 month ago 1 By unlord 3 years 1 month ago Normal topic Images By Jon Awbrey 3 years 1 month ago 1 By unlord 3 years 1 month ago Normal topic report spam button By kohlhase 3 years 1 month ago

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Open archived version from archive - Welcome to PlanetMath | planetmath.org

the following protocol for account registration Please email the site admin Joe Corneli at holtzermann17 gmail com and tell him a little about yourself including the username you want He ll then activate an account for you Many thanks PlanetMath org Ltd PS Although we will usually be faster please note that it may take up for one week for a membership request to be processed Search form Search Home

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Open archived version from archive - User account | planetmath.org

in Request new password active tab Username or e mail address Search form Search Home Articles Questions Forums Planetary Bugs HS Secondary University Tertiary Graduate Advanced Industry Practice Research Topics LaTeX help Math Comptetitions Math History Math Humor PlanetMath Comments

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Open archived version from archive - field arising from special relativity | planetmath.org

plays for the velocities of the bodies the role of the infinity These velocities v π£ thus satisfy always v c π£ π By 1 we get c c c c v c formulae sequence direct sum π π π direct sum π π£ π for v c π£ π so c π behaves like the infinity One can define the mapping f β c c S π β π π π by setting f x c tanh x assign π π₯ π π₯ 2 which is easily seen to be a bijection Define also the binary operation direct product for the numbers u v π’ π£ of the open interval c c π π by u v c tanh artanh u c artanh v c direct product π’ π£ π artanh π’ π artanh π£ π 3 Then the system S π direct sum direct product may be checked to be a ring and the bijective mapping 2 to be homomorphic f x y f x f y f x y f x f y formulae sequence π π₯ π¦ direct sum π π₯ π π¦ π π₯ π¦ direct product π π₯ π π¦ Consequently the system S π direct sum direct product as the homomorphic image of the field β β also itself is a field Baker 1 calls the numbers of the set S π i e c c π π the Einstein numbers References 1 G A Baker Jr Einstein numbers Amer Math Monthly 61 1954 39 41 2 H T Davis College algebra Prentice Hall N Y 1940 351 3 T Gregor J HaluΕ‘ka Two dimensional Einstein numbers and associativity arXiv 2013 Type of Math Object Topic Major Section Reference Parent examples of fields Add a correction Attach a problem Ask a question Search

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Open archived version from archive - pahio | planetmath.org

s paradox Gauss Lucas theorem Gaussian sum Gelfand Tornheim theorem general associativity general commutativity general formulas for integration general power general solution of linear differential equation generalisation of Gaussian integral generalized binomial coefficients generating function of Hermite polynomials generating function of Laguerre polynomials generating function of Legendre polynomials generators of inverse ideal generatrices of hyperbolic paraboloid generatrices of one sheeted hyperboloid geometric constructions by Euclid geometric sequence gradient theorem graph of equation xy constant greatest common divisor of several integers Gronwall s theorem group of units grouping method for factoring polynomials groups in field growth of exponential function Gudermannian function half factorial ring Halley s formula harmonic conjugate function harmonic division harmonic mean in trapezoid Heaviside formula Hensel s lemma for integers Hermite equation Hermite numbers Hermite polynomials Heron s principle Heronian mean is between geometric and arithmetic mean higher order derivatives of sine and cosine Hjalmar Mellin holomorphic function associated with continuous function holomorphic mapping of curve and tangent homogeneous equation homogeneous linear differential equation homomorphic image of group hyperbola hyperbolas orthogonal to ellipses hyperbolic sine integral ideal decomposition in Dedekind domain ideal generators in Pr ufer ring ideal inverting in Pr ufer ring ideal multiplication laws ideal norm ideal of elements with finite order identity element is unique identity theorem of power series image equation image ideal of divisor imaginary quadratic field implications of having divisor theory improper limits incircle radius determined by Pythagorean triple independence of characteristic polynomial on primitive element independence of valuations indirect proof of identity theorem of power series induction proof of fundamental theorem of arithmetic inequality with absolute values infimum and supremum of sum and product infinite product of differences 1 a i infinite product of sums 1 a i inflexion point injection can be extended to isomorphism integer contraharmonic means integer harmonic means integral basis of quadratic field integral closure is ring integral element integral equation integral of limit function integral over a period interval integral over plane region integral related to arc sine integral sign integrals of even and odd functions integration of sqrt x 2 1 integration of fraction power expressions integration of Laplace transform with respect to parameter integration of rational function of sine and cosine integration under integral sign integrity characterized by places intercept theorem intersection of quadratic surface and plane intersection of sphere and plane inverse Gudermannian function inverse Laplace transform of derivatives inverse Laplace transform of meromorphic function inverse number inverse of a product inversion of plane invertibility of regularly generated ideal invertible formal power series invertible ideal is finitely generated irreducibility of binomials with unity coefficients irreducible of a UFD is prime irreducible polynomial irreducible polynomials over finite field isepiphanic inequality isocline isogonal trajectory isolated subgroup isomorphism swapping zero and unity isoperimetric problem iterated limit in mathbb R 2 Jacobian and chain rule Kalle V ais al a Kempner series Klein 4 ring Krull valuation Krull valuation domain Kummer s acceleration method Kustaa Inkeri Lambert series lamellar field Laplace integrals Laplace transform of t nf t Laplace transform of frac f t t Laplace transform of convolution Laplace transform of cosine and sine Laplace transform of derivative Laplace transform of Dirac delta Laplace transform of integral Laplace transform of logarithm Laplace transform of periodic functions Laplace transform of power function Laplace transform of sine integral Laplace transforms of derivatives Laurent expansion of rational function least and greatest value of function least and greatest zero least common multiple least surface of revolution Legendre s theorem on angles of triangle Lehmer mean Leibniz estimate for alternating series lemma for imaginary quadratic fields lengths of angle bisectors lengths of triangle medians level curve limit examples limit function of sequence limit of geometric sequence limit of nondecreasing sequence limit of nth root of n limit of real number sequence limit of sequence as sum of series limit rules of functions limits of natural logarithm Lindel of hypothesis line in space line of curvature line through an intersection point linear differential equation of first order linear formulas for Pythagorean triples list of improper integrals locus logarithm series logarithmic integral logarithmic scale logarithmic spiral loxodrome Lying Over Theorem manipulating convergent series mantissa function maximal ideal is prime maximal ideals of ring of formal power series mean curvature at surface point mean square deviation mean value theorem for several variables median of trapezoid Mellin s inverse formula method of integrating factors methods of evaluating improper integrals Meusnier s theorem midpoint minimal and maximal number minimal surface minimality property of Fourier coefficients mixed fraction morphic number motion in central force field multiples of an algebraic number multiplication of series multiplication rule gives inverse ideal multiplicatively independent multiplicity mutual positions of vectors nabla acting on products natural numbers are well ordered natural projection negation nested interval theorem Niels Henrik Abel non constant element of rational function field non existence of universal series convergence criterion non isomorphic completions of mathbb Q non isomorphic groups of given order non uniformly continuous function norm and trace of algebraic number norm Euclidean number field normal curvatures normal line normal of plane normal section nth root by Newton s method nth root formulas number number field that is not norm Euclidean number of prime ideals in a number field numerator and denominator increased by same amount octant ODE types reductible to the variables separable case ODE types solvable by two quadratures on inhomogeneous second order linear ODE with constant coefficients one sided continuity one sided continuity by series one sided derivatives opposite number opposite polynomial order of factors in infinite product order of products order of six means order of vanishing order valuation ordered group orders in a number field orders of elements in integral domain orthogonal circles orthogonal curve orthogonality of Chebyshev polynomials orthogonality of Laguerre polynomials orthogonality of Legendre polynomials osculating curve ostensibly discontinuous antiderivative Ostrowski s valuation theorem overring p adic canonical form p adic valuation parallel and perpendicular planes parallelism of line and plane parallelism of two planes parallellism in Euclidean plane parallelogram principle parallelogram

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Open archived version from archive - Carmichael numbers - 561 (contd) | planetmath.org

05 57 This application is valid for not only x 2 1 but also for other quadratic polynomials including non monic ones Members can refer to earlier message pertaining to the case x 2 1 for the algorithm Log in to post comments pseudoprimality of powers Permalink Submitted by akdevaraj on Mon 07 20 2015 05 20 We can use pari to find the bases for which powers are pseudoprimes Example 25 is pseudoprime to the bases 7 18 and 24 Log in to post comments Isomorphism an example Permalink Submitted by akdevaraj on Sat 07 25 2015 10 31 2 5n 1 31 is an infinite group isomorphic with Z 31 Here n belongs to N Log in to post comments Isomorphism an example Permalink Submitted by akdevaraj on Sat 07 25 2015 10 31 2 5n 1 31 is an infinite group isomorphic with Z 31 Here n belongs to N Log in to post comments Isomorphism Permalink Submitted by pahio on Sat 07 25 2015 13 21 Deva can you please explain in detail which is the infinite group you mean I see only the expression 2 5 n 1 31 superscript 2 5 n 1 31 frac 2 5n 1 31 The group β€ 31 subscript β€ 31 mathbb Z 31 is finite Log in to post comments Isomorphism an example Permalink Submitted by akdevaraj on Mon 07 27 2015 05 02 Pahio I meant the finite group of remainders mod 31 sorry I typed Γ―nfinite Log in to post comments Which isomorphism Permalink Submitted by pahio on Mon 07 27 2015 17 09 Ok β€ 31 subscript β€ 31 mathbb Z 31 is an additive group of order 31 and forms in fact a field since 31 is prime But I am interested which isomorphism you are speaking of The expression 2 5 n 1 31 superscript 2 5 n 1 31 frac 2 5n 1 31 says me nothing excuse me Log in to post comments Which isomorphism Permalink Submitted by pahio on Mon 07 27 2015 17 11 Ok β€ 31 subscript β€ 31 mathbb Z 31 is an additive group of order 31 and forms in fact a field since 31 is prime But I am interested which isomorphism you are speaking of The expression 2 5 n 1 31 superscript 2 5 n 1 31 frac 2 5n 1 31 says me nothing excuse me Log in to post comments which isomorphism Permalink Submitted by pahio on Mon 07 27 2015 17 23 Ok β€ 31 subscript β€ 31 mathbb Z 31 is an additive group of order 31 and in fact a Galois field since 31 is prime But I m interested in the isomorphism you are speaking of The expression 2 5 n 1 31 superscript 2 5 n 1 31 frac 2 5n 1 31 says me nothing excuse me Log in to post comments Message system Permalink Submitted by pahio on Mon 07 27 2015 17 28

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Open archived version from archive