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Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

RSA numbers are difficult to-factor composite numbers having exactly two prime factors (i.e., so-called semiprimes) that were listed in the Factoring Challenge of RSA ...

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).

If a is a point in the open unit disk, then the Blaschke factor is defined by B_a(z)=(z-a)/(1-a^_z), where a^_ is the complex conjugate of a. Blaschke factors allow the ...

The Feit-Thompson conjecture asserts that there are no primes p and q for which (p^q-1)/(p-1) and (q^p-1)/(q-1) have a common factor. Parker noticed that if this were true, ...

A Hajós group is a group for which all factorizations of the form (say) Z_n=A direct sum B have A or B periodic, where the period is a divisor of n. Hajós groups arose after ...

Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It ...

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

A characteristic factor is a factor in a particular factorization of the totient function phi(n) such that the product of characteristic factors gives the representation of a ...