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 ...

- 86 3. PROOFS OF THE THEOREMS. PROOF OF THEOREM 1. Assume t-hat A, B, G e G

2

Ck;> and le

t* r s I s„ r s^ A = 1 1 k

Si ri. , B = 2 2 [2 2. ,0 = 3 3 ks^ r 3 3. such that dl) A

n + B

n = G

n. By Lemma 1 we obtain A — M N M N 1 1 , B

n2 2 3 3 kN M , B

nkN M > ^ — kN M 1 1 2 2 3 3 where ír +s Vjr]

n+fr -s VT"] Mm m J ^ in m J I C12) N =2VjT Hence by (11) we have i— ír +s ViP]

n-ír -s VT"

1]" , m=l,2,: H TO m J I. TO m J J C13) M. = M + 3 12 N„ = N

4 + N . 3 12 From C12) and C13) we get (r

1+s

1Vir]

n+(r

2+s

2Vir]

n = [ly^Vk-jV Putting in the last equality a = r

1+s

i VIT, ß « r

2+s

2VjT, y = r

3+s

3VT, we obtain a

r'+ ß

n= I