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A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness, and ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

The quotient space X/∼ of a topological space X and an equivalence relation ∼ on X is the set of equivalence classes of points in X (under the equivalence relation ∼) ...

A number n is said to be divisible by d if d is a divisor of n. The function Divisible[n, d] returns True if an integer n is divisible by an integer d. The product of any n ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.

A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

A number n with prime factorization n=product_(i=1)^rp_i^(a_i) is called k-almost prime if it has a sum of exponents sum_(i=1)^(r)a_i=k, i.e., when the prime factor ...