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The Mandelbar set is a fractal set analogous to the Mandelbrot set or its generalization to a higher power with the variable z replaced by its complex conjugate z^_.

A modification of the Eberhart's conjecture proposed by Wagstaff (1983) which proposes that if q_n is the nth prime such that M_(q_n) is a Mersenne prime, then ...

An emirp ("prime" spelled backwards) is a prime whose (base 10) reversal is also prime, but which is not a palindromic prime. The first few are 13, 17, 31, 37, 71, 73, 79, ...

Let N be an odd integer, and assume there exists a Lucas sequence {U_n} with associated Sylvester cyclotomic numbers {Q_n} such that there is an n>sqrt(N) (with n and N ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...

In a game proposed by J. H. Conway, a devil chases an angel on an infinite chessboard. At each move, the devil can eliminate one of the squares, and the angel can make a leap ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

When ac is divisible by a number b that is relatively prime to a, then c must be divisible by b.

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...