This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α∈R and for any γ∈R and ε>0 there are infinitely many pairs of coprime integers m,n such that |nα-m-γ |≦ 1/|n|^1-ε. This improves upon previously known results, in which the exponent of approximation was at best 1/2.

Research supported by EPSRC grant EP/J00149X/1.