Search Results for ""

If p is a prime >3, then the numerator of the harmonic number H_(p-1)=1+1/2+1/3+...+1/(p-1) (1) is divisible by p^2 and the numerator of the generalized harmonic number ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

A number n is called an e-perfect number if sigma_e(n)=2n, where sigma_e(n) is the sum of the e-Divisors of n. If m is squarefree, then sigma_e(m)=m. As a result, if n is ...

Let a divisor d of n be called a 1-ary (or unitary) divisor if d_|_n/d (i.e., d is relatively prime to n/d). Then d is called a k-ary divisor of n, written d|_kn, if the ...

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 ...

A von Neumann regular ring is a ring R such that for all a in R, there exists a b in R satisfying a=aba (Jacobson 1989, p. 196). More formally, a ring R is regular in the ...

There are several definitions of "almost Hamiltonian" in use. As defined by Punnim et al. (2007), an almost Hamiltonian graph is a graph on n nodes having Hamiltonian number ...

A camel graph is a graph formed by all possible moves of a hypothetical chess piece called a "camel" which moves analogously to a knight except that it is restricted to moves ...

A caterpillar graph, caterpillar tree, or simply "caterpillar," is a tree in which every graph vertex is on a central stalk or only one graph edge away from the stalk (in ...