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In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

A Ruth-Aaron pair is a pair of consecutive numbers (n,n+1) such that the sums of the prime factors of n and n+1 are equal. They are so named because they were inspired by the ...

Anomalous cancellation is a "canceling" of digits of a and b in the numerator and denominator of a fraction a/b which results in a fraction equal to the original. Note that ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...