829n

829n is a mathematical expression used to denote the set of all multiples of 829 obtained by multiplying 829 by an integer n. In this sense, for any integer n, the value 829n belongs to the set { …, -1658, -829, 0, 829, 1658, … }. The coefficient 829 being a fixed positive integer means that every member of the set is divisible by 829.

As an arithmetic progression, the set 829n has a common difference of 829. It also forms a subgroup of the integers under addition, consisting precisely of the integers that are congruent to 0 modulo 829. In number-theoretic terms, the greatest common divisor of any two elements 829n and 829m is 829 times the greatest common divisor of n and m, i.e., gcd(829n, 829m) = 829·gcd(n, m). The smallest positive element in the set is 829.

In modular arithmetic, the statement x ≡ 0 (mod 829) holds exactly when x is of the form 829n for some integer n. The notation is commonly used when describing divisibility, solving linear congruences, or parameterizing families of numbers in algebraic contexts.

Beyond mathematics, the string “829n” may appear as a model number, code, or identifier in technical documents or product catalogs, where its meaning is determined entirely by context and unrelated to its mathematical interpretation.