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The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...

The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base and top side lengths of the truncated pyramid be a and b, and let the ...

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

A notation for large numbers due to Steinhaus (1999). In circle notation, is defined as n in n squares, where numbers written inside squares (and triangles) are interpreted ...

Let omega(n) be the number of distinct prime factors of n. If Psi(x) tends steadily to infinity with x, then lnlnx-Psi(x)sqrt(lnlnx)<omega(n)<lnlnx+Psi(x)sqrt(lnlnx) for ...

The sequence composed of 1s and 2s obtained by starting with the number 1, and picking subsequent elements to avoid repeating the longest possible substring. The first few ...

Let n-1=FR where F is the factored part of a number F=p_1^(a_1)...p_r^(a_r), (1) where (R,F)=1, and R<sqrt(n). Pocklington's theorem, also known as the Pocklington-Lehmer ...

Let alpha be a nonzero rational number alpha=+/-p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L), where p_1, ..., p_L are distinct primes, alpha_l in Z and alpha_l!=0. Then ...

A lattice path from one point to another is p-good if it lies completely below the line y=(p-1)x. (1) Hilton and Pederson (1991) show that the number of p-good paths from (1, ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...