Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1989. 19/8. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 19)

K. Dialek — A . Grytzuk: Some remarks on certain diophontine equations

- 23 Let d=|ja

o,a

s, . . . > a

nJ » | rre | > 4-, m X d and suppose that C2.6) has at least two solutions. Let C2.7) <

xk'y

k> * Z > k-i.2, . . . denote the sequence of solutions of (2.6>. The sequence C2.7) will be called regular if Ca) for every i<k, det Cb> for every i<k„ K - VI k ' m * o det [x. , y

t K > = i We prove the following theorem: THEOREM 1

. Let N

4 denote the number of regular solutions of C2,6> and let |m|>l , m-fd, where d=fa .„a^ , . . . , a J. Then c 2. e ) N £ n

. PROO

F

. Suppose that the equation C2.6) has N > n regular solutions <x

1,y

1>, <x

2,y

2>, ... , < x

n+

1,y

n,

t>, then from C2.6> we get C2. 9) a x

n+a x

n_

1y + oi 11 71 a x^ax" 4y' + O 2 12 2 +a y? = m r>

J 1 y^ ea m n 2 +a x

n"*y + ... +a y" On*! 1 n+i - n + 1 rr'n + l The fundamental determinant of the system C2.P> has the foi^m