Additive Number Theory

Also found in: Wikipedia

0.02 sec.

the section of number theory specifically concerned with the expansion of natural numbers 1, 2, 3, . . . into components of definite characteristics. Best known are such problems as expressing a number as a sum of four squares, nine cubes, and so on (known as Waring’s problem) and expressing a number as a sum of a prime number and two squares. A general analytical method worked out by G. Hardy and J. Littlewood in England and I. A. Vinogradov in the USSR is used for the solution of additive types of problems. Many additive number theory problems can be solved by means of elementary methods, particularly by the method of addition of sequences proposed by L. G. Shnirel’man. Iu. V. Linnik has solved a number of problems in this area with the help of the dispersion method developed by him.

B. M. BREDIKHIN

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.

?Page tools

Printer friendly
Cite / link

Feedback

Mentioned in	?		References in periodicals archive	?		Encyclopedia browser	?		Full browser	?
No references found			Topics include Ramsey number theory (that there cannot be complete disorder and in any large system there must always be some structure), additive number theory, multiplicative number theory, combinatorial games, sequences, elementary number theory and graph theory. Combinatorial number theory; proceedings by SciTech Book News			addition agent addition formula addition item addition polymer addition polymerization addition polymers Addition Reaction addition record addition resin addition sign addition solid solution addition table additional service authorization additional services Additions Additive additive alternate additive fabrication additive factor additive function additive gene action additive genetic variance additive identity additive inverse additive level Additive Number Theory additive primary colors additive process additive set function additive synthesis Additives additus maximus addorsed addra Address address bar address book address bus address cleansing address computation address constant address conversion address counter address decoder address field address format address generation address interleaving Address Language address lookup utilities address mask			Additive function Additive Gaussian white noise additive gene action additive gene action additive gene action additive gene action additive genetic relationship additive genetic relationship additive genetic relationship additive genetic relationship additive genetic variance additive genetic variance additive genetic variance additive genetic variance additive genetic variance additive identity additive identity Additive Increase Additive Decrease Additive Increase Rate Additive Increase Rate Factor Additive Increase, Multiplicative Decrease additive inverse additive inverse additive inverse additive level Additive Manufacturing Users Group Additive Modular Knowledge Base Additive Multi-Resolution Source Code Additive notation Additive notation Additive Number Theory Additive Operational Product Additive operator Additive operator Additive operator Additive operator Additive operator Additive primary color Additive Primary Colors Additive Primary Colors additive process additive process Additive Pulse Modelocked Additive Quark Model Additive Random Utility Model additive relationship additive relationship additive relationship additive relationship Additive Requirements additive set function Additive Solution Additive Spread-Spectrum Additive synthesis Additive System of Photographic Exposure Additive Truncated Gaussian Noise Additive Two DMARD Additive Upper Bound Additive Waveguide Grating Additive White Gaussian Additive White Gaussian Channel

Encyclopedia

Free Tools:	For surfers: Free toolbar & extensions \| Word of the Day \| Help For webmasters: Free content \| Linking \| Lookup box \| Double-click lookup

Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.