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In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

A map x|->x^p where p is a prime.

An integer n is called a super unitary perfect number if sigma^*(sigma^*(n))=2n, where sigma^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... ...

If a number fails Miller's primality test for some base a, it is not a prime. If the number passes, it may be a prime. A composite number passing Miller's test is called a ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

A modification of Legendre's formula for the prime counting function pi(x). It starts with |_x_| = (1) where |_x_| is the floor function, P_2(x,a) is the number of integers ...

A number is squareful, also called nonsquarefree, if it contains at least one square in its prime factorization. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

Diagonalize a form over the rationals to diag[p^a·A,p^b·B,...], where all the entries are integers and A, B, ... are relatively prime to p. Then the p-signature of the form ...