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- Modular_arithmetic abstract "In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.For a positive integer n, two integers a and b are said to be congruent modulo n, and written asif their difference a − b is an integer multiple of n (or n divides a − b). The number n is called the modulus of the congruence, while integers congruent to a modulo n are creating a set called congruence class, residue class or simply residue of the integer a, modulo n.".
- Modular_arithmetic thumbnail Clock_group.svg?width=300.
- Modular_arithmetic wikiPageExternalLink jbmodart.htm.
- Modular_arithmetic wikiPageExternalLink id.php?id=3545.
- Modular_arithmetic wikiPageExternalLink modular_arithmetic.
- Modular_arithmetic wikiPageExternalLink whitney.
- Modular_arithmetic wikiPageExternalLink modular-arithmetic.
- Modular_arithmetic wikiPageExternalLink Modulo.shtml.
- Modular_arithmetic wikiPageExternalLink Spear.
- Modular_arithmetic wikiPageExternalLink Gauss_Modular.pdf.
- Modular_arithmetic wikiPageExternalLink aaprover.page.
- Modular_arithmetic wikiPageID "20087".
- Modular_arithmetic wikiPageRevisionID "605380592".
- Modular_arithmetic hasPhotoCollection Modular_arithmetic.
- Modular_arithmetic id "p/c024850".
- Modular_arithmetic title "Congruence".
- Modular_arithmetic title "Modular Arithmetic".
- Modular_arithmetic urlname "ModularArithmetic".
- Modular_arithmetic subject Category:Finite_rings.
- Modular_arithmetic subject Category:Group_theory.
- Modular_arithmetic subject Category:Modular_arithmetic.
- Modular_arithmetic type Abstraction100002137.
- Modular_arithmetic type Attribute100024264.
- Modular_arithmetic type FiniteRings.
- Modular_arithmetic type Property104916342.
- Modular_arithmetic type Ring104981658.
- Modular_arithmetic type Sound104981139.
- Modular_arithmetic type SoundProperty104983122.
- Modular_arithmetic comment "In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.".
- Modular_arithmetic label "Arithmétique modulaire".
- Modular_arithmetic label "Aritmetica modulare".
- Modular_arithmetic label "Aritmética modular".
- Modular_arithmetic label "Aritmética modular".
- Modular_arithmetic label "Arytmetyka modularna".
- Modular_arithmetic label "Kongruenz (Zahlentheorie)".
- Modular_arithmetic label "Modulair rekenen".
- Modular_arithmetic label "Modular arithmetic".
- Modular_arithmetic label "Сравнение по модулю".
- Modular_arithmetic label "حسابيات نمطية".
- Modular_arithmetic label "合同式".
- Modular_arithmetic label "同餘".
- Modular_arithmetic sameAs Modulární_aritmetika.
- Modular_arithmetic sameAs Kongruenz_(Zahlentheorie).
- Modular_arithmetic sameAs Aritmética_modular.
- Modular_arithmetic sameAs Kongruentzia_(zenbaki-teoria).
- Modular_arithmetic sameAs Arithmétique_modulaire.
- Modular_arithmetic sameAs Aritmetica_modulare.
- Modular_arithmetic sameAs 合同式.
- Modular_arithmetic sameAs 합동_(대수학).
- Modular_arithmetic sameAs Modulair_rekenen.
- Modular_arithmetic sameAs Arytmetyka_modularna.
- Modular_arithmetic sameAs Aritmética_modular.
- Modular_arithmetic sameAs m.051f3.
- Modular_arithmetic sameAs Q319400.
- Modular_arithmetic sameAs Q319400.
- Modular_arithmetic sameAs Modular_arithmetic.
- Modular_arithmetic wasDerivedFrom Modular_arithmetic?oldid=605380592.
- Modular_arithmetic depiction Clock_group.svg.
- Modular_arithmetic isPrimaryTopicOf Modular_arithmetic.