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The nth root of the denominator B_n of the nth convergent A_n/B_n of a number x tends to a constant lim_(n->infty)B_n^(1/n) = e^beta (1) = e^(pi^2/(12ln2)) (2) = 3.275823... ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A pseudoprime is a composite number that passes a test or sequence of tests that fail for most composite numbers. Unfortunately, some authors drop the "composite" ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

Although Bessel functions of the second kind are sometimes called Weber functions, Abramowitz and Stegun (1972) define a separate Weber function as ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...