Two Applications of a Result of S. Chowla

Abstract

In this paper, I give two applications of the following result of Chowla [2]:

Let {m, n} denote the number of different pairs of numbers x, y such that (x, y) = 1, 1 ≤ x ≤ m, 1 ≤ y ≤ n.

Then

{m, n} = 6mn/Ï€² + O(m log n) if m ≥ n.