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Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...

A Latin square is said to be odd if it contains an odd number of rows and columns that are odd permutations. Otherwise, it is said to be even. Let the number of even Latin ...

Polynomial identities involving sums and differences of like powers include x^2-y^2 = (x-y)(x+y) (1) x^3-y^3 = (x-y)(x^2+xy+y^2) (2) x^3+y^3 = (x+y)(x^2-xy+y^2) (3) x^4-y^4 = ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example, p_1 = {3,8,5,10,9,4,6,1,7,2} (1) p_2 = ...

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...