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A extension ring (or ring extension) of a ring R is any ring S of which R is a subring. For example, the field of rational numbers Q and the ring of Gaussian integers Z[i] ...

Given the Lucas sequence U_n(b,-1) and V_n(b,-1), define Delta=b^2+4. Then an extra strong Lucas pseudoprime to the base b is a composite number n=2^rs+(Delta/n), where s is ...

Each of the sacred unit fractions which the ancient Egyptians attributed to the six parts of the eye of the god Horus: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions, ...

In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while the numerator and denominator of continued ...

A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers: 1 = 1! (1) 2 = 2! (2) 145 = 1!+4!+5! (3) 40585 = ...

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...

A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...

The formal term used for a collection of objects. It is denoted {a_i}_(i in I) (but other kinds of brackets can be used as well), where I is a nonempty set called the index ...

The sequence of six 9s which begins at the 762nd decimal place of pi, pi=3.14159...134999999_()_(six 9s)837... (Wells 1986, p. 51). The positions of the first occurrences of ...

A fibered category F over a topological space X consists of 1. a category F(U) for each open subset U subset= X, 2. a functor i^*:F(U)->F(V) for each inclusion i:V↪U, and 3. ...