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 ...

- 89 I^F [M-M"]For n=2k (22) R = a

2 and S=0. follows. By C20) and (22) we getA

n= 0 1 n n a

2 0 n n 1 0 a 0 . o a

2. . 0 1 Similarly we obtain B

n = b

2. For n=dm we have 1 0 0 1 C

n = c

2. A

4m.

D4m 2 m +ti =a 1 0 0 1 1 0 0 1 1 0 0 1 = (a

2Tr

i+b

2

r"] . 1 0 0 1 1 0 0 1 = c

4

m and the proof is complete. From Theorem 2 we get the following Corollary: COROLLAR

Y CR.Z.Domiaty [3]) If K=Q and a,b,c <s Z then the equation A

4 + B? = C

4 a b e have infinitely solutions of the form A.[2 hlK-ii £]>

c*=[° b ] where a=^m

2-n

2].l, b=2mnl, c= |m

2+n

2]

.1, m>n, Cm,n)=l, 12:1