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 ...

- 87 where ex, ft,? e Q ^VIPj . Now, let a,ft,y e Q ^VlP j . Then we can write and a = r^s^/lT

, ft = r

2+s

2VT, y = r^+s^VT a = r

1-s

iV)T, J5 - r

2-s

2-vr, f = r

3-s

3Vr\ wit-h integers r , s , m=l,2,3. ° m* m' ' From the assumption we have a

r

i+ It is easy to see that Ca) r'+ C Thus we obtain ci4> J- + I - \ [r

n

+r") > and (IS) Donote 2V1P ^ ° ^ ^VTT"

1 ^ ^ J ^VT"' ^ ] * 2 VIT

1 2YjT C16> M

x= I (aW],M

2= I [/3

n+?T],M

3- £ (/Vp)

. C17> N = 1 2YT From this and from C14>,C1S) we have C18) M

3 = ti

± + M

2, Consider the matrices A^»

1

8!»^ o

f* form N = N + N . 3 12 M1 M ".1 M N Al= kN l ' Bi = 2 kN > Cl = 3 3 kN M l l 2 2. 3 3 where N m=l,2,3.