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Midy's theorem

Index Midy's theorem

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period. [1]

15 relations: Base (exponentiation), Decimal, Duodecimal, Elementary algebra, Fraction (mathematics), France, Group theory, Kenneth A. Ross, Mathematician, Mathematics, Modular arithmetic, Octal, Parity (mathematics), Prime number, Repeating decimal.

Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

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Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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Duodecimal

The duodecimal system (also known as base 12 or dozenal) is a positional notation numeral system using twelve as its base.

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Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

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Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

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France

France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Kenneth A. Ross

Kenneth Allen Ross (born January 21, 1936) is a mathematician and a emeritus professor of mathematics at University of Oregon.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.

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Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

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Midy s theorem, Midy theorem, Midy's Theorem.

References

[1] https://en.wikipedia.org/wiki/Midy's_theorem

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