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A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...

Find the maximum number of bishops B(n) that can be placed on an n×n chessboard such that no two attack each other. The answer is 2n-2 (Dudeney 1970, Madachy 1979), giving ...

A binary unit of information equal to 8 bits. Unfortunately, the storage of binary numbers in computers is not entirely standardized. Because computers store information in ...

The Connell sequence is the sequence obtained by starting with the first positive odd number (1), taking the next two even numbers (2, 4), the next three odd numbers (5, 7, ...

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

According to Hardy and Wright (1979), the 44-digit Ferrier's prime determined to be prime using only a mechanical calculator, is the largest prime found before the days of ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...