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A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

Thâbit ibn Kurrah's rules is a beautiful result of Thâbit ibn Kurrah dating back to the tenth century (Woepcke 1852; Escott 1946; Dickson 2005, pp. 5 and 39; Borho 1972). ...

Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...

The unknot, also called the trivial knot (Rolfsen 1976, p. 51), is a closed loop that is not knotted. In the 1930s Reidemeister first proved that knots exist which are ...

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

The Wagner graph is a name sometimes given to the 4-Möbius ladder (Bondy and Murty 2008, pp. 275-276). The association arises through the theorem of Wagner (1937) that graphs ...