Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Bui Minh Phong: Recurrence sequences and pseudoprimes

Theorem 1.5. ([10]) LetU - U{L,M) be a non-degenerate Lehmer sequence with the condition (L,M

) = 1. Let k> \ be an integer. Then all solutions of the Diophantine equation Ufr !U

X- sy

q in integers s e S, y * 0, q > 2 satisfy max(x,|ji?>M)<Q for\y\>\ and max(x,\s\,\L\,\M\,k)<C

7 for the case when \y\= 1, kx > 6, (k;x) * (2;4),(2;5), where C

6 and C

7 are effectively computable constants, C

6 depends only L, M,k and S, C

7 depends only on S

. Hieorem 1.6. ([10]) LetU = U(L,M) be a non-degenerate Lehmer sequence. Then the equation \U

X\=\U„\ has non solutions in non-negative integers x,y with x^y andmax(x,y)> min(e

39

8 , 2 6

7 log|4M|). 1.4. Lucas primitive roots Let R = R(A,B) be a Lucas sequence defined by integers = 0, = 1, A, B and the recursion 121