modular arithmetic oor Nederlands
modular arithmetic
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system of algebraic operations defined for remainders under division by a fixed positive integer; system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus
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This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic.
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Modular arithmetic is used to describe events that occur in regular cycles.
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This brings us to modular arithmetic, also known as clock arithmetic.
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Modular arithmetic, for instance, is used to describe the functioning of electrical generators and gasoline engines in mathematical terms.
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Leonhard Euler considered algebraic operations on numbers modulo an integer, modular arithmetic, in his generalization of Fermat's little theorem.
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Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.
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Steps 4 and 5 can be performed with the extended Euclidean algorithm; see modular arithmetic.
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Steps 4 and 5 can be performed with the extended Euclidean algorithm; see modular arithmetic.
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Steps 4 and 5 can be performed with the extended Euclidean algorithm (en); see modular arithmetic.
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A well-known example of modular arithmetic is clock face arithmetic.
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The distinctive feature of prime numbers is the following: division is possible in modular arithmetic if and only if n is a prime.
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The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field.
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Examples of such functions are very classical - the Jacobi theta functions and the Fourier coefficients of Siegel modular forms of genus two - but it is a relatively recent observation that the Jacobi forms have an arithmetic theory very analogous to the usual theory of modular forms.
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He also made important contributions to number theory with his 1801 book Disquisitiones arithmeticae, which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity.
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In joint work with George Lusztig, Deligne applied étale cohomology to construct representations of finite groups of Lie type; with Michael Rapoport, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms.
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