Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/11)

Krystyna Bialek — Aleksander Grytczuk: The equation of Fermat in ...

- 88 By (18) we have A + B = C . l l l From the above equality and from Lemma 1 and Lemma 3 we obtain that there exist the matrices A,B,G such that A

± = A , B

i = B" , C

t = G' = A

n and therefore we have A

n + B

n = G

n

. Thus A,B,C are matrices of the form A = r s r l l ks r , B = 2 2 ks r , G = 3 3 ks_ r l 2 2_ 3 3_ hence A,B,C <£ G 2 C k ) , what gives the proof of the Theorem. PROOF OF THEOREM 2

. Let C19> A = r s as r then by Lemma 1 we have (20) r s n R S as r aS R where (21) R = I j^[r+sV^J

n+^r-sVSrJ

n|, Putting in C21) r=0, s=l we get =4-