5n

5n denotes the product of the integer 5 and another variable n. In mathematics, it is most commonly used to express a multiple of five. For integer n, the value of 5n is an integer that is divisible by 5.

As a set, {5n | n ∈ Z} equals 5Z, the subgroup of the integers consisting of all multiples of 5. If the domain is natural numbers including zero, it is {0, 5, 10, 15, …}.

Solving 5n = k: there is a solution with integer n iff k is a multiple of 5; otherwise no integer solution. When k is a multiple of 5, the solution is n = k/5.

In modular arithmetic, 5n ≡ 0 (mod 5) for all n. More generally, modulo m, the values of 5n depend on gcd(5, m); for example modulo 10, 5n cycles through 0 and 5.

In algebra and number theory, 5n is a basic linear term used in equations, factorization, and the description of arithmetic progressions. It should not be confused with 5^n, the exponential function. The expression is widely used to denote a multiple of five and to describe properties related to divisibility and linear relations.