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The positive integers 1, 2, 3, ..., equivalent to N.

The nonnegative integers 0, 1, 2, ....

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...

A number n is said to be divisible by d if d is a divisor of n. The function Divisible[n, d] returns True if an integer n is divisible by an integer d. The product of any n ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

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.

The maximum cardinal number of a collection of subsets of a t-element set T, none of which contains another, is the binomial coefficient (t; |_t/2_|), where |_x_| is the ...