Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Diophantine approximation with square-free integers

Glyn Harmana1

a1 Imperial College, London

In this paper we shall prove the following two results.

Theorem 1. Let xs220A > 0 and β a real number be given. Them, for almost all real a (in the sense of Lebesque measure), there are infinitely many pairs of square-free integers m, n such that

S0305004100061685_eqn1

(Received September 13 1983)

(Revised November 21 1983)