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- Linear_congruence_theorem abstract "In modular arithmetic, the question of when a linear congruence can be solved is answered by the linear congruence theorem. If a and b are any integers and n is a positive integer, then the congruencehas a solution for x if and only if b is divisible by the greatest common divisor d of a and n (denoted by gcd(a,n)). When this is the case, and x0 is one solution of (1), then the set of all solutions is given byIn particular, there will be exactly d = gcd(a,n) solutions in the set of residues {0,1,2,...,n − 1}. The result is a simple consequence of Bézout's identity.".
- Linear_congruence_theorem wikiPageExternalLink congruence.
- Linear_congruence_theorem wikiPageID "18700".
- Linear_congruence_theorem wikiPageRevisionID "597369375".
- Linear_congruence_theorem hasPhotoCollection Linear_congruence_theorem.
- Linear_congruence_theorem subject Category:Modular_arithmetic.
- Linear_congruence_theorem subject Category:Theorems_in_number_theory.
- Linear_congruence_theorem type Abstraction100002137.
- Linear_congruence_theorem type Communication100033020.
- Linear_congruence_theorem type Message106598915.
- Linear_congruence_theorem type Proposition106750804.
- Linear_congruence_theorem type Statement106722453.
- Linear_congruence_theorem type Theorem106752293.
- Linear_congruence_theorem type TheoremsInNumberTheory.
- Linear_congruence_theorem comment "In modular arithmetic, the question of when a linear congruence can be solved is answered by the linear congruence theorem. If a and b are any integers and n is a positive integer, then the congruencehas a solution for x if and only if b is divisible by the greatest common divisor d of a and n (denoted by gcd(a,n)).".
- Linear_congruence_theorem label "Linear congruence theorem".
- Linear_congruence_theorem label "Lineare Kongruenz".
- Linear_congruence_theorem label "Teorema de congruencia lineal".
- Linear_congruence_theorem label "Théorème de congruence linéaire".
- Linear_congruence_theorem label "نظرية التطابق الخطية".
- Linear_congruence_theorem label "线性同余方程".
- Linear_congruence_theorem sameAs Lineare_Kongruenz.
- Linear_congruence_theorem sameAs Teorema_de_congruencia_lineal.
- Linear_congruence_theorem sameAs Théorème_de_congruence_linéaire.
- Linear_congruence_theorem sameAs m.04q_3.
- Linear_congruence_theorem sameAs Q524257.
- Linear_congruence_theorem sameAs Q524257.
- Linear_congruence_theorem sameAs Linear_congruence_theorem.
- Linear_congruence_theorem wasDerivedFrom Linear_congruence_theorem?oldid=597369375.
- Linear_congruence_theorem isPrimaryTopicOf Linear_congruence_theorem.