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A factorization of the form 2^(4n+2)+1=(2^(2n+1)-2^(n+1)+1)(2^(2n+1)+2^(n+1)+1). (1) The factorization for n=14 was discovered by Aurifeuille, and the general form was ...

The second part of Pollard rho factorization method concerns detection of the fact that a sequence has become periodic. Pollard's original suggestion was to use the idea ...

Define an emirpimes ("semiprime" spelled backwards) as a semiprime whose (base 10) reversal is a different semiprime. The first such number is 15, because 15 reversed is 51 ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

The Riemann-Siegel formula is a formula discovered (but not published) by Riemann for computing an asymptotic formula for the Riemann-Siegel function theta(t). The formula ...

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 ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the ...