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The elliptic logarithm is generalization of integrals of the form int_infty^x(dt)/(sqrt(t^2+at)), for a real, which can be expressed in terms of logarithmic and inverse ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters ...

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

The number of bases in which 1/p is a repeating decimal (actually, repeating b-ary) of length l is the same as the number of fractions 0/(p-1), 1/(p-1), ..., (p-2)/(p-1) ...

Consider a Lucas sequence with P>0 and Q=+/-1. A Fibonacci pseudoprime is a composite number n such that V_n=P (mod n). There exist no even Fibonacci pseudoprimes with ...

A Pascal's triangle written in a square grid and padded with zeros, as written by Jakob Bernoulli (Smith 1984). The figurate number triangle therefore has entries a_(ij)=(i; ...

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...

A flexagon-like structure created by connecting the ends of a strip of four squares after folding along 45 degrees diagonals. Using a number of folding movements, it is ...