négyzetszámok

Négyzetszámok, also known as perfect squares, are integers that are the square of another integer. In other words, a number 'n' is a négyzetszám if there exists an integer 'k' such that n = k². The sequence of négyzetszámok begins with 0 (0²), 1 (1²), 4 (2²), 9 (3²), 16 (4²), 25 (5²), and so on. The négyzetszámok are always non-negative. The term "négyzetszám" is the Hungarian word for "square number". The concept is fundamental in number theory and appears in various mathematical contexts, including algebra, geometry, and combinatorics. For instance, the area of a square with side length 's' is s², making the area a négyzetszám if 's' is an integer. Properties of négyzetszámok include that their last digit can only be 0, 1, 4, 5, 6, or 9. Also, the difference between consecutive négyzetszámok increases linearly: 1-0=1, 4-1=3, 9-4=5, 16-9=7, etc., forming a sequence of odd numbers. Determining if a given number is a négyzetszám often involves checking if its square root is an integer.