Square the square into a square in 21 steps

Mathematicians have made great efforts in the past, but achieved no results. As a result, in 1930, the famous Soviet mathematician Lukin speculated that it was impossible to divide a square into a finite number of squares of different sizes. Mollen challenged this conjecture and proposed a solution: if a rectangle has two different square partitions, where each square in one partition is different from each square in the other partition, then adding two squares (which are different from any square in either partition) to the two partitions will produce a perfect square. Prior to this, there were