Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1994. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 22)

HERENDI, T. and PETHŐ, A., Trinomials, which are divisible by quadratic polynomials

Trinomials, which are divisible by quadratic polynomials 73 We devide the set of pairs a,b £ Z intő two classes according as (i) &

77

1"

1 mod

2-/m1 M

2) = 0; (ii) 6

m_1 mod

2-/

m_ 1 (a,6

2) 5é 0. In the case (i) by Lemma 2 (b) the values of a,b are explicitely determinable and so the possible values of A are infinit

ely many but they are explicitely determinable as a series. In the case (ii) we can simplify the équation by b

m~

l mod 2 • fm-i (a, and with the simplified eqation can be solved in the same way as in (a). References [1] E. DOBROWOLSKI, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. [2] T. N. SHOREY and R. TiJDEMAN, Exponential diophantine équations, Cambridge University Press

, Cambridge • London • New York • New Rochelle • Melbourne • Sydney, (1986). [3] K. F. ROTH, Rational approximations to algebraic numbers, Mathematika

, 2 (1955), 1-20. [4] P. RlBENBOIM, On the factorization of x

n - Bx - A, Enseign. Math., 37 (1991), 191-200. [5] A. SCHINZEL, On reducible polynomials, (to appear).