In a right triangle, the Pythagorean Theorem states that the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle). If we denote the lengths of the two legs as \( m \) and \( n \), and the length of the hypotenuse as \( c \), the relationship can be expressed as:
\[ m^2 + n^2 = c^2 \]
So, to fill in the blank in your equation, it would be:
\[ m^2 + n^2 = c^2 \]