The term perfect square is used in mathematics in two meanings:

• a positive integer which is the square of some other integer, i.e. can be written in the form n² for some integer n. See square number.
• an algebraic expression that can be factored as the square of some other expression, e.g. a² ± 2ab + b² = (a ± b)².

This is not the same as a magic square.