18 = 3 3 2 + 2 = 3
Because of the lemma mentioned above, = 2 + 3 2 then we get
= ( 2 − 9 2 ) = 3 ( 2 − 2 )
Therefore, the expression for 18 w becomes
r 3 = 18 w = 54 f ( e 2 − f 2 ) = 54 f ( e + f ) ( e − f ) = 3 3 ×2 f ( e + f ) ( e − f ).
Use the similar method above, because the three factors of r 3 are all coprime, they can be expressed as
−2 = 3 + = 3 − = 3 Which also yields a solution 3 + 3 + 3 = 0 . Finally, be the argument of infinite descent, the original solution x , y , z is impossible.
Then, the proof for Fermat’s last theorem when n =3 is done.
Conclusion
As a concluded above, Persistence and endurance are the most common points between Shackleton’s expedition and Wiles’s proof of Fermat’s last theorem. As we can see, being persistence with something you like and never giving up will eventually lead to a day when you will reach the highest mountain in your heart. The process of fighting the difficulties is the process you beat and surpass yourself again and again. Last but not least, to all the readers, Rome was not built in one day, one need to be unremitting with one’s dream so that one can realize it.
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