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Let p be an odd prime and b a positive integer not divisible by p. Then for each positive odd integer 2k-1<p, let r_k be r_k=(2k-1)b (mod p) with 0<r_k<p, and let t be the ...

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

For a real number x, the mantissa is defined as the positive fractional part x-|_x_|=frac(x), where |_x_| denotes the floor function. For example, for x=3.14159, the mantissa ...

An integer which is expressible in only one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in more than one way, it ...

For a given n, is the problem of determining if a set is mortal solvable? n=1 is solvable, n=2 is unknown, and n>=3 is unsolvable.

A negative matrix is a real or integer matrix (a)_(ij) for which each matrix element is a negative number, i.e., a_(ij)<0 for all i, j. Negative matrices are therefore a ...

Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1. The ring of ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...