Search Results for ""

Let B_k be the kth Bernoulli number and consider nB_(n-1)=-1 (mod n), where the residues of fractions are taken in the usual way so as to yield integers, for which the ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...