A simple proof on the Fermat’s last theorem in cases of n=3k (k=1,2,3……)

Abstract

Using simple mathematics of middle school and “the disprove method”, the paper discusses a special case of x=y of the Fermat’s last theorem, but strangely, if x=y, from Diophantine equation it derives an impossible equality 2=1, therefore, it is reasonable to suggest that with respect to Fermat’s last theorem, it should supplement a restriction of x =y = z. Moreover, all the positive integers which is bigger than 2 can be represented by n=3k; n=3k+1; and n=3k+2 (k=1,2,3, ……), on the basis of the proof on the Fermat’s last theorem in case of n=3, using the mathematical induction and “the disprove method” the paper proves that the theorem is also true for all cases of n=3k (k=1,2,3,……).