About: Fermat's factorization method

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Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation. Indeed, if is a factorization of N, then Since N is odd, then c and d are also odd, so those halves are integers. (A multiple of four is also a difference of squares: let c and d be even.)

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rdfs:label	Fermat's factorization method (en)
rdfs:comment	Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation. Indeed, if is a factorization of N, then Since N is odd, then c and d are also odd, so those halves are integers. (A multiple of four is also a difference of squares: let c and d be even.) (en)
sameAs	Fermat's factorization method Fermat's factorization method
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Cite_journal dbt:Math dbt:Mvar dbt:Not_a_typo dbt:Refimprove dbt:Reflist dbt:Number_theoretic_algorithms
Subject	Integer factorization algorithms
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Fermat's_factorization_method?oldid=1072619468&ns=0
Wikipage page ID	2132433 (xsd:integer)
page length (characters) of wiki page	10347 (xsd:nonNegativeInteger)
Wikipage revision ID	1072619468 (xsd:integer)
Link from a Wikipage to another Wikipage	Program synthesis Table of Gaussian integer factorizations Unique factorization domain Algebra Monoid factorisation Semiprime General number field sieve Integer factorization algorithms Difference of two squares Pierre de Fermat Quadratic sieve Prime number Completing the square Parity (mathematics) Pascal's triangle FOIL method Factor theorem Factorization Factorization of polynomials Integer Integer factorization Modular arithmetic Euler's factorization method Rational number Recursion (computer science)
has abstract	Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation. Indeed, if is a factorization of N, then Since N is odd, then c and d are also odd, so those halves are integers. (A multiple of four is also a difference of squares: let c and d be even.) In its simplest form, Fermat's method might be even slower than trial division (worst case). Nonetheless, the combination of trial division and Fermat's is more effective than either. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Fermat's_factorization_method
is Wikipage redirect of	Fermat's method Fermat factorisation Fermat factorization Fermat factorization method
is Link from a Wikipage to another Wikipage of	List of things named after Pierre de Fermat Difference of two squares Dixon's factorization method Daniel Shanks List of eponyms (A–K) Congruence of squares List of algorithms Ganita Kaumudi Factorization Integer factorization Euler's factorization method Fermat's method Fermat factorisation Fermat factorization Fermat factorization method
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Fermat's_factorization_method

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