Fermat, a French mathematician in the 17th century read thoroughly a copy of "Arithmetica", an ancient Greek book on mathematics and added many notes in the margin. He wrote down 48 theorems there. Since then, mathematicians proved one theorem after another. His last theorem simply states that three positive integers X, Y and Z cannot satisfy the equation of X

^{n}+ Y

^{n}= Z

^{n} when n is greater than two. But this theorem remained unproved for nearly 360 years until Wiles, an English mathematician finally found the proof in 1995. The proof was 108 pages long and used many difficult mathematical methods, which only professional can understand. It is anticipated that a new and simple proof will be found. We like to add below our note and proposition, which we get a hint from Fermat's last theorem. We are confident about this, but have neither proof nor counterexample.