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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 ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

A statistic which assigns a single number to several individual statistics in order to quantify trends. The best-known index in the United States is the consumer price index, ...

Let G_1, G_2, ..., G_t be a t-graph edge coloring of the complete graph K_n, where for each i=1, 2, ..., t, G_i is the spanning subgraph of K_n consisting of all graph edges ...

Define the juggler sequence for a positive integer a_1=n as the sequence of numbers produced by the iteration a_(k+1)={|_a_k^(1/2)_| for even a_k; |_a_k^(3/2)_| for odd a_k, ...

Legendre's conjecture asserts that for every n there exists a prime p between n^2 and (n+1)^2 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398). It is one of ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

The sequence defined by e_0=2 and the quadratic recurrence equation e_n=1+product_(i=0)^(n-1)e_i=e_(n-1)^2-e_(n-1)+1. (1) This sequence arises in Euclid's proof that there ...