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For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

Let K be a number field, then each fractional ideal I of K belongs to an equivalence class [I] consisting of all fractional ideals J satisfying I=alphaJ for some nonzero ...

A function defined for all positive integers, sometimes also called an arithmetic function (Nagell 1951, p. 26) or number theoretic function (Wilf 1994, p. 58).

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

A set having the largest number k of distinct residue classes modulo m so that no subset has zero sum.

The series with sum sum_(n=0)^infty1/(F_(2^n))=1/2(7-sqrt(5)), where F_k is a Fibonacci number (Honsberger 1985).

The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.

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

Every "large" even number may be written as 2n=p+m where p is a prime and m in P union P_2 is the set of primes P and semiprimes P_2.

The number 2^(1/3)=RadicalBox[2, 3] (the cube root of 2) which is to be constructed in the cube duplication problem. This number is not a Euclidean number although it is an ...