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A set of positive integers S is called sum-free if the equation x+y=z has no solutions x, y, z in S. The probability that a random sum-free set S consists entirely of odd ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

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 sum of powers of even divisors of a number. It is the analog of the divisor function for even divisors only and is written sigma_k^((e))(n). It is given simply in terms ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...

The Gaussian joint variable theorem, also called the multivariate theorem, states that given an even number of variates from a normal distribution with means all 0, (1) etc. ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

Let rho(x) be an mth degree polynomial which is nonnegative in [-1,1]. Then rho(x) can be represented in the form {[A(x)]^2+(1-x^2)[B(x)]^2 for m even; ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

A near-perfect matching is a matching in which a single vertex is left unmatched. Just as perfect matchings can occur only for graphs with an even number of vertices, ...