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In 1657, Fermat posed the problem of finding solutions to sigma(x^3)=y^2, and solutions to sigma(x^2)=y^3, where sigma(n) is the divisor function (Dickson 2005). The first ...

A power floor prime sequence is a sequence of prime numbers {|_theta^n_|}_n, where |_x_| is the floor function and theta>1 is real number. It is unknown if, though extremely ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

A (0,1)-matrix is an integer matrix in which each element is a 0 or 1. It is also called a logical matrix, binary matrix, relation matrix, or Boolean matrix. The number of ...

The number obtained by adding the reciprocals of the odd twin primes, B=(1/3+1/5)+(1/5+1/7)+(1/(11)+1/(13))+(1/(17)+1/(19))+.... (1) By Brun's theorem, the series converges ...

The operator I^~ which takes a real number to the same real number I^~r=r.

An even alternating permutation number, more commonly called a tangent number.

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

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 ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...