4n2

4n^2 is a mathematical expression representing four times the square of an integer n. Because 4n^2 = (2n)^2, it is the square of an even integer, and consequently is always a nonnegative perfect square. For integer n, 4n^2 is divisible by 4.

The sequence formed by 4n^2 as n varies over the integers is the set of even squares: 0, 4, 16, 36, 64, 100, ... The general term is a_n = 4n^2. In modular arithmetic, 4n^2 ≡ 0 (mod 4) for all n; modulo 8 it is 0 when n is even and 4 when n is odd.

In algebra and number theory, 4n^2 appears in identities and factorizations such as x^2 − 4n^2 = (x − 2n)(x + 2n). It also describes the area of a square with side length 2n, linking a simple algebraic expression to a geometric interpretation. The form 4n^2 is commonly used in problems involving even squares or when expressing a perfect square that is a multiple of 4.