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Polite number

Index Polite number

In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. [1]

22 relations: Bijection, Bijective proof, Concrete Mathematics, Cribbage, Divisor, Fermat number, Fibonacci Quarterly, James Joseph Sylvester, Lambek–Moser theorem, Mersenne prime, Natural number, Number theory, Parity (mathematics), Partition (number theory), Perfect number, Power of two, Prime number, Stairs, Trapezoid, Triangular number, William J. LeVeque, Young tableau.


In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Bijective proof

In combinatorics, bijective proof is a proof technique that finds a bijective function f: A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, thus proving that they have the same number of elements, |A|.

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Concrete Mathematics

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, first published in 1989, is a textbook that is widely used in computer-science departments as a substantive but light-hearted treatment of the analysis of algorithms.

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Cribbage, or crib, is a card game traditionally for two players, but commonly played with three, four or more, that involves playing and grouping cards in combinations which gain points.

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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

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Fermat number

In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.

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Fibonacci Quarterly

The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year.

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James Joseph Sylvester

James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician.

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Lambek–Moser theorem

In combinatorial number theory, the Lambek–Moser theorem is a generalization of Beatty's theorem that defines a partition of the positive integers into two subsets from any monotonic integer-valued function.

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Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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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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Partition (number theory)

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.

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Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

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Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

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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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A stairway, staircase, stairwell, flight of stairs, or simply stairs is a construction designed to bridge a large vertical distance by dividing it into smaller vertical distances, called steps.

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In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

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Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.

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William J. LeVeque

William Judson LeVeque (August 9, 1923 – December 1, 2007) was an American mathematician and administrator who worked primarily in number theory.

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Young tableau

In mathematics, a Young tableau (plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.

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Staircase number, Trapezoidal number.


[1] https://en.wikipedia.org/wiki/Polite_number

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