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The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

Landau's problems are the four "unattackable" problems mentioned by Landau in the 1912 Fifth Congress of Mathematicians in Cambridge, namely: 1. The Goldbach conjecture, 2. ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

Pre-Algebra

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...