16n

16n denotes the algebraic expression obtained by multiplying 16 by an integer n. In standard usage, n is taken from the integers Z, though in many contexts n is restricted to natural numbers N. The value 16n is therefore a multiple of 16, and the set {16n | n ∈ Z} is the subgroup 16Z of the integers.

Properties of 16n include closure under addition and subtraction: 16n + 16m = 16(n + m) and 16n − 16m = 16(n − m). The product of two such terms is (16n)(16m) = 256nm, which is a multiple of 256. In prime factor terms, 16n = 2^4 · n, so the exponent of 2 in 16n equals 4 plus the 2-adic valuation v2(n). Consequently, the divisibility structure of 16n depends on n's factors of 2.

Examples illustrate the sequence: n = 0 yields 0, n = 1 yields 16, n = 2 yields 32, and n = −3 yields −48. In modular arithmetic, 16n is always congruent to 0 modulo 16, reflecting its divisibility by 16.

Applications of the expression appear in mathematics and computer science. It describes arithmetic progressions with common difference 16, and it often appears in contexts involving memory alignment or block sizes that are multiples of 16. It is important to distinguish 16n from hexadecimal notation, where 16 denotes a base; here 16n is simply the product of the integer 16 and n.