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The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...

Given the left factorial function Sigma(n)=sum_(k=1)^nk!, SK(p) for p prime is the smallest integer n such that p|1+Sigma(n-1). The first few known values of SK(p) are 2, 4, ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

A superior highly composite number is a positive integer n for which there is an e>0 such that (d(n))/(n^e)>=(d(k))/(k^e) for all k>1, where the function d(n) counts the ...

The tetranacci numbers are a generalization of the Fibonacci numbers defined by T_0=0, T_1=1, T_2=1, T_3=2, and the recurrence relation T_n=T_(n-1)+T_(n-2)+T_(n-3)+T_(n-4) ...

Trigonometric functions of npi/13 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 13 is not a ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...

The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...