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Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian ...

Take K a number field and L an Abelian extension, then form a prime divisor m that is divided by all ramified primes of the extension L/K. Now define a map phi_(L/K) from the ...

An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

A Colbert number is any prime number with more than 1000000 decimal digits whose discovery contributes to the long-sought after proof that k=78557 is the smallest Sierpiński ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

To divide is to perform the operation of division, i.e., to see how many times a divisor d goes into another number n. n divided by d is written n/d or n÷d. The result need ...