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A Belphegor number (also known as a Beelphegor number or a beastly palindromic prime) is a palindromic number of the form 1(0...)666(0...)1. Numbers of this form are named ...

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

The number of "prime" boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

Let p_n/q_n be the sequence of convergents of the continued fraction of a number alpha. Then a Brjuno number is an irrational number such that ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).