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The divisors of 10 illustrated with Cuisenaire rods: 1, 2, 5, and 10. In mathematics, a divisor of an integer , also called a factor of , is an integer that may be multiplied by some integer to produce . [1] In this case, one also says that is a multiple of .
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
Elementary Evaluation of Certain Convolution Sums Involving Divisor Functions PDF of a paper by Huard, Ou, Spearman, and Williams. Contains elementary (i.e. not relying on the theory of modular forms) proofs of divisor sum convolutions, formulas for the number of ways of representing a number as a sum of triangular numbers, and related results.
A cultural divide is "a boundary in society that separates communities whose social economic structures, opportunities for success, conventions, styles, are so different that they have substantially different psychologies". [1]
In the ring /, the residue class ¯ is a zero divisor since ¯ ¯ = ¯ = ¯.; The only zero divisor of the ring of integers is .; A nilpotent element of a nonzero ring is always a two-sided zero divisor.