<image>Given that \( m \geq 2 \), \( n \geq 2 \), and both \( m \) and \( n \) are positive integers, if \( m^{n} \) is "decomposed" in the same manner as shown in the bottom-right, then the following three statements are:
(1) In the decomposition of \( 2^{5} \), the largest number is ___;
(2) In the decomposition of \( 4^{3} \), the smallest number is ___;
(3) If the smallest number in the decomposition of \( m^{3} \) is 31, then \( m \) is equal to ___.
