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Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory

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This page provides a list of all articles available at PlanetMath in the following topic:

11-XX Number theory.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

11-00 General reference works (handbooks, dictionaries, bibliographies, etc.) edit

AdamSmithee 09:31, 16 January 2006 (UTC)[reply]
CryptoDerk 14:29, May 2, 2005 (UTC)
CryptoDerk 14:47, May 2, 2005 (UTC)
There should also be a link to the method from Modular arithmetic - AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
Can be used to expand properties AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
CryptoDerk 17:41, May 2, 2005 (UTC)
CryptoDerk 17:58, May 2, 2005 (UTC)
linas 22:12, 12 Mar 2005 (UTC)
CryptoDerk 18:00, May 2, 2005 (UTC)
CryptoDerk 18:09, May 2, 2005 (UTC)
Hv 08:58, 5 August 2005 (UTC)[reply]
CryptoDerk 20:53, May 2, 2005 (UTC)
Charles Matthews 10:26, 25 October 2005 (UTC)[reply]
CryptoDerk 18:27, May 3, 2005 (UTC)
linas 23:53, 12 Mar 2005 (UTC)
Jeekc 11:25, 8 November 2005 (UTC)[reply]
Jeekc 11:25, 8 November 2005 (UTC)[reply]
Could use a remark on generalizing to gcd of more than 2 numbers AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
see also greatest common divisor - AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
linas 22:40, 12 Mar 2005 (UTC)
  • PM: mean, id=3028 -- WP: mean -- Status: A
Jeekc 11:25, 8 November 2005 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
  • PM: pi, id=432 -- WP guess: pi -- Status:
AdamSmithee 09:31, 16 January 2006 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
Hv 09:18, 5 August 2005 (UTC)[reply]
linas 00:34, 13 Mar 2005 (UTC)
Not a particularly illuminating proof AdamSmithee 13:02, 5 January 2006 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 13:02, 5 January 2006 (UTC)[reply]
CryptoDerk 22:20, Mar 12, 2005 (UTC)
linas 23:49, 12 Mar 2005 (UTC)
Charles Matthews 10:30, 25 October 2005 (UTC)[reply]
AdamSmithee 08:39, 8 March 2006 (UTC)[reply]
AdamSmithee 08:39, 8 March 2006 (UTC)[reply]

11-01 Instructional exposition (textbooks, tutorial papers, etc.) edit

Simon12 02:49, 30 July 2006 (UTC)[reply]
AdamSmithee 13:10, 5 January 2006 (UTC)[reply]

11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors edit

linas 00:31, 13 Mar 2005 (UTC)
linas 23:18, 12 Mar 2005 (UTC)
linas 00:37, 13 Mar 2005 (UTC)
Jeekc 11:32, 8 November 2005 (UTC)[reply]
Jeekc 11:32, 8 November 2005 (UTC)[reply]
Jeekc 11:32, 8 November 2005 (UTC)[reply]
linas 23:24, 12 Mar 2005 (UTC)
linas 00:28, 13 Mar 2005 (UTC)
Can be used to clarify the affirmation in the WP article, which is already challenged in the Talk section AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
AdamSmithee 09:37, 16 January 2006 (UTC)[reply]
linas 00:40, 13 Mar 2005 (UTC)
linas 23:14, 12 Mar 2005 (UTC)

11A07 Congruences; primitive roots; residue systems edit

AdamSmithee 13:15, 5 January 2006 (UTC)[reply]
Hv 09:07, 5 August 2005 (UTC)[reply]
linas 22:37, 12 Mar 2005 (UTC)
Still needs TeX attention beyond my abilities. Jtwdog 17:33, 28 October 2005 (UTC)[reply]
PM article has a better wording than WP AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
linas 00:45, 13 Mar 2005 (UTC)

11A15 Power residues, reciprocity edit

linas 23:26, 12 Mar 2005 (UTC)
AdamSmithee 14:06, 5 January 2006 (UTC)[reply]
WP proof never actually shows that if a is not a quadratic residue mod p then a(p − 1)/2 ≡ −1 (mod p), so it could be combined with the PM proof AdamSmithee 14:06, 5 January 2006 (UTC)[reply]
linas 00:56, 13 Mar 2005 (UTC)

11A25 Arithmetic functions; related numbers; inversion formulas edit

AdamSmithee 14:23, 5 January 2006 (UTC)[reply]
linas 22:35, 12 Mar 2005 (UTC)
linas 22:55, 12 Mar 2005 (UTC)
Jtwdog 17:32, 28 October 2005 (UTC)[reply]
linas 22:57, 12 Mar 2005 (UTC)
linas 23:04, 12 Mar 2005 (UTC)
linas 23:01, 12 Mar 2005 (UTC)
PM has some more examples which could be used AdamSmithee 14:23, 5 January 2006 (UTC)[reply]
linas 23:11, 12 Mar 2005 (UTC)
Chenxlee (talk) 18:58, 25 September 2008 (UTC)[reply]
linas 01:14, 13 Mar 2005 (UTC)
WP redirect to be removed linas 23:08, 12 Mar 2005 (UTC)

11A41 Primes edit

linas 16:53, 4 July 2006 (UTC)[reply]
Composite elements of integral domains AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
linas 00:58, 13 Mar 2005 (UTC)
linas 16:26, 4 July 2006 (UTC)[reply]
linas 00:58, 13 Mar 2005 (UTC)
linas 01:02, 13 Mar 2005 (UTC)
AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
  • PM: emirp, id=9415new! -- WP guess: emirp -- Status:

11A51 Factorization; primality edit

linas 01:08, 13 Mar 2005 (UTC)

11A55 Continued fractions edit

linas 22:53, 12 Mar 2005 (UTC)
linas 22:51, 12 Mar 2005 (UTC)

11A63 Radix representation; digital problems edit

linas 01:12, 13 Mar 2005 (UTC)

11A67 Other representations edit

linas 23:39, 12 Mar 2005 (UTC)

11A99 Miscellaneous edit

linas 01:25, 13 Mar 2005 (UTC)

11Axx Elementary number theory edit

11B05 Density, gaps, topology edit

11B13 Additive bases edit

11B25 Arithmetic progressions edit

by Charles Matthews. Oleg Alexandrov 16:21, 15 July 2005 (UTC)[reply]

11B34 Representation functions edit

Chenxlee (talk) 19:01, 25 September 2008 (UTC)[reply]

11B37 Recurrences edit

CryptoDerk 22:25, Feb 1, 2005 (UTC)

11B39 Fibonacci and Lucas numbers and polynomials and generalizations edit

AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
linas 03:27, 13 Mar 2005 (UTC)
I added an external link AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
I added an external link AdamSmithee 09:00, 8 March 2006 (UTC)[reply]

11B50 Sequences (mod $m$) edit

11B57 Farey sequences; the sequences $$ edit

11B65 Binomial coefficients; factorials; $q$-identities edit

11B68 Bernoulli and Euler numbers and polynomials edit

linas 01:19, 14 July 2005 (UTC)[reply]

11B73 Bell and Stirling numbers edit

11B75 Other combinatorial number theory edit

11B83 Special sequences and polynomials edit

11B85 Automata sequences edit

linas 02:13, 13 Mar 2005 (UTC)
minor merge, just copy the relation on the genering function.linas 02:13, 13 Mar 2005 (UTC)

11B99 Miscellaneous edit

linas 02:18, 13 Mar 2005 (UTC)
minor, just copy the table linas 02:16, 13 Mar 2005 (UTC)

11Bxx Sequences and sets edit

11C08 Polynomials edit

linas 02:21, 13 Mar 2005 (UTC)
Doctormatt 06:37, March 13, 2007 (UTC)

11C99 Miscellaneous edit

11Cxx Polynomials and matrices edit

11D09 Quadratic and bilinear equations edit

linas 01:17, 13 Mar 2005 (UTC)
linas 01:19, 13 Mar 2005 (UTC)

11D25 Cubic and quartic equations edit

11D41 Higher degree equations; Fermat's equation edit

linas 01:22, 13 Mar 2005 (UTC)

11D68 Rational numbers as sums of fractions edit

11D72 Equations in many variables edit

11D79 Congruences in many variables edit

AdamSmithee 09:54, 16 January 2006 (UTC)[reply]
AdamSmithee 09:54, 16 January 2006 (UTC)[reply]

11D85 Representation problems edit

11D99 Miscellaneous edit

easy merge, copy the stuff about algorithm linas 02:34, 13 Mar 2005 (UTC)

11Dxx Diophantine equations edit

11E04 Quadratic forms over general fields edit

11E08 Quadratic forms over local rings and fields edit

11E10 Forms over real fields edit

11E12 Quadratic forms over global rings and fields edit

11E16 General binary quadratic forms edit

11E25 Sums of squares and representations by other particular quadratic forms edit

11E39 Bilinear and Hermitian forms edit

11E57 Classical groups edit

11E76 Forms of degree higher than two edit

11E81 Algebraic theory of quadratic forms; Witt groups and rings edit

11E88 Quadratic spaces; Clifford algebras edit

copy the part about filter algebra linas 02:38, 13 Mar 2005 (UTC)

11Exx Forms and linear algebraic groups edit

11F06 Structure of modular groups and generalizations; arithmetic groups edit

The PM intro lends a nice concreteness to the abstract proceedings in WP. linas 02:43, 13 Mar 2005 (UTC)

11F11 Modular forms, one variable edit

linas 02:49, 13 Mar 2005 (UTC)
The redirect to Hecke operator should be undone. Or one could merge. linas 02:49, 13 Mar 2005 (UTC)
Why? Charles Matthews 19:53, 25 October 2005 (UTC)[reply]
linas 02:49, 13 Mar 2005 (UTC)

11F30 Fourier coefficients of automorphic forms edit

The PM article is badly mis-classified. linas 02:51, 13 Mar 2005 (UTC)

11F67 Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols edit

PM article is mis-classified linas 02:56, 13 Mar 2005 (UTC)
linas 02:59, 13 Mar 2005 (UTC)

11F80 Galois representations edit

11Fxx Discontinuous groups and automorphic forms edit

11G05 Elliptic curves over global fields edit

11G07 Elliptic curves over local fields edit

11Gxx Arithmetic algebraic geometry (Diophantine geometry) edit

11H06 Lattices and convex bodies edit

actually, just copy the graphic diagram over linas 03:01, 13 Mar 2005 (UTC)
The rigorous defn in PM is much nicer than the prose in WP. linas 03:04, 13 Mar 2005 (UTC)

11H46 Products of linear forms edit

11H55 Quadratic forms (reduction theory, extreme forms, etc.) edit

11Hxx Geometry of numbers edit

11J04 Homogeneous approximation to one number edit

11J06 Markov and Lagrange spectra and generalizations edit

11J61 Approximation in non-Archimedean valuations edit

11J68 Approximation to algebraic numbers edit

Chenxlee (talk) 02:19, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:27, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:30, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:30, 9 July 2008 (UTC)[reply]

11J70 Continued fractions and generalizations edit

11J71 Distribution modulo one edit

linas 03:06, 13 Mar 2005 (UTC)

11J72 Irrationality; linear independence over a field edit

Chenxlee (talk) 02:32, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:41, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:41, 9 July 2008 (UTC)[reply]

11J81 Transcendence (general theory) edit

linas 01:36, 14 July 2005 (UTC)[reply]
KimJ, the owner of this article, mentioned to me that this was a joke entry. I concur. Even though it's true, this "theorem" doesn't go by this name except as a joke. CryptoDerk 02:48, Feb 2, 2005 (UTC)

11J82 Measures of irrationality and of transcendence edit

11J85 Algebraic independence; Gelfond's method edit

11J86 Linear forms in logarithms; Baker's method edit

11Jxx Diophantine approximation, transcendental number theory edit

11K06 General theory of distribution modulo $1$ edit

11K16 Normal numbers, radix expansions, etc. edit

11K38 Irregularities of distribution, discrepancy edit

11K45 Pseudo-random numbers; Monte Carlo methods edit

11K99 Miscellaneous edit

11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms edit

11L03 Trigonometric and exponential sums, general edit

11L05 Gauss and Kloosterman sums; generalizations edit

linas 03:18, 13 Mar 2005 (UTC)
Jtwdog 17:57, 28 October 2005 (UTC)[reply]

11L40 Estimates on character sums edit

11Lxx Exponential sums and character sums edit

11M06 $\zeta (s)$ and $L(s, \chi)$ edit

linas 22:47, 12 Mar 2005 (UTC)
linas 20:40, 2 June 2006 (UTC)[reply]
linas 22:49, 12 Mar 2005 (UTC)
linas 20:18, 2 June 2006 (UTC)[reply]

11M20 Real zeros of $L(s, \chi)$; results on $L(1, \chi)$ edit

11M35 Hurwitz and Lerch zeta functions edit

11M41 Other Dirichlet series and zeta functions edit

11M99 Miscellaneous edit

11Mxx Zeta and $L$-functions: analytic theory edit

11N05 Distribution of primes edit

linas 03:40, 13 Mar 2005 (UTC)
linas 03:35, 13 Mar 2005 (UTC)
linas 03:42, 13 Mar 2005 (UTC)
linas 03:32, 13 Mar 2005 (UTC)

11N13 Primes in progressions edit

11N25 Distribution of integers with specified multiplicative constraints edit

11N32 Primes represented by polynomials; other multiplicative structure of polynomial values edit

AdamSmithee 15:35, 7 February 2006 (UTC)[reply]

11N35 Sieves edit

11N36 Applications of sieve methods edit

11N37 Asymptotic results on arithmetic functions edit

11N56 Rate of growth of arithmetic functions edit

11N80 Generalized primes and integers edit

11N99 Miscellaneous edit

11Nxx Multiplicative number theory edit

11P05 Waring's problem and variants edit

11P32 Goldbach-type theorems; other additive questions involving primes edit

11P81 Elementary theory of partitions edit

The PM article has a nice proof of the theorem. linas 01:28, 13 Mar 2005 (UTC)

11P99 Miscellaneous edit

11Pxx Additive number theory; partitions edit

11R04 Algebraic numbers; rings of algebraic integers edit

The PM article is more pleasently rigorous/clearer. linas 01:35, 13 Mar 2005 (UTC)
linas 01:32, 13 Mar 2005 (UTC)
It might be easier to just copy, and throw away the current WP article. linas 01:44, 13 Mar 2005 (UTC)
edited, actually ... the PM article is structured better, and is easier to read. linas 01:42, 13 Mar 2005 (UTC)

11R06 PV-numbers and generalizations; other special algebraic numbers edit

11R11 Quadratic extensions edit

11R16 Cubic and quartic extensions edit

11R18 Cyclotomic extensions edit

linas 01:46, 13 Mar 2005 (UTC)

11R20 Other abelian and metabelian extensions edit

11R21 Other number fields edit

11R27 Units and factorization edit

PM article is mis-categorized, needs to be with other p-adic topics linas 04:06, 13 Mar 2005 (UTC)

11R29 Class numbers, class groups, discriminants edit

Jtwdog 17:54, 28 October 2005 (UTC)[reply]
linas 01:49, 13 Mar 2005 (UTC)
Jtwdog 17:54, 28 October 2005 (UTC)[reply]
Jtwdog 17:54, 28 October 2005 (UTC)[reply]

11R32 Galois theory edit

Jeekc 11:35, 8 November 2005 (UTC)[reply]

11R34 Galois cohomology edit

11R37 Class field theory edit

11R42 Zeta functions and $L$-functions of number fields edit

11R44 Distribution of prime ideals edit

11R45 Density theorems edit

11R52 Quaternion and other division algebras: arithmetic, zeta functions edit

11R56 Adèle rings and groups edit

linas 03:47, 13 Mar 2005 (UTC)
linas 03:49, 13 Mar 2005 (UTC)

11R58 Arithmetic theory of algebraic function fields edit

11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.) edit

11R99 Miscellaneous edit

linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 03:54, 13 Mar 2005 (UTC)

11Rxx Algebraic number theory: global fields edit

11S15 Ramification and extension theory edit

11S20 Galois theory edit

11S25 Galois cohomology edit

11S31 Class field theory; $p$-adic formal groups edit

11S80 Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) edit

11S99 Miscellaneous edit

11Sxx Algebraic number theory: local and $p$-adic fields edit

11T23 Exponential sums edit

11T30 Structure theory edit

11T55 Arithmetic theory of polynomial rings over finite fields edit

11T71 Algebraic coding theory; cryptography edit

11T99 Miscellaneous edit

11Txx Finite fields and commutative rings (number-theoretic aspects) edit

11Y05 Factorization edit

11Y11 Primality edit

11Y40 Algebraic number theory computations edit

11Y55 Calculation of integer sequences edit

11Y65 Continued fraction calculations edit

11Y99 Miscellaneous edit

11Yxx Computational number theory edit

11Z05 Miscellaneous applications of number theory edit

linas 22:21, 12 Mar 2005 (UTC)
Charles Matthews 10:48, 25 October 2005 (UTC)[reply]
Charles Matthews 10:48, 25 October 2005 (UTC)[reply]
Charles Matthews 10:49, 25 October 2005 (UTC)[reply]
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