Let c IN. For d with gcd (d, c) = 1 let (d, c) be defined by d (d, c) = 1 mod c, 1 (d, c) c. Let s, t IN with 1 s c, 1 t c. The main result is that for arbitrary fixed > 0, but uniformly over c, s and t, #{d IN : (c, d) = 1, 1 d s and 1 (d, c) t} = (c)/c2 st + O (c1/2+). Equivalently, the points (d, (c, d)) are approximately uniformly distributed in [0, c] [0, c]: The two -dimensional discrepancy of {(d, (c, d)): 1 d c and (c, d) = 1} in [0, c] [0, c] is O (c-1/2).
