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 ...

- 85 PROOF From the assumption we have C9) a b n R S c d kS R for some n£2 and By Lemma 2 we have CIO) a b c d f

4(a) f Cd> where f Ca) - fjCd) = Ca—d) From C9) and CIO) we obtain f

4 Ca) f

±Cd) R S kS R Thus f Ca) = f

4 Cd) = R, = kS, = S. From this we have f^a) - f 1 Cd) = 0. Since Si*Q, then we obtain and hence c = kb. On the other hand Ca-d)^

i = f^a) ~ f

1

Cd;

> ~ By the fact that 1-0 w

e g«t a=d and the proof is complete.