The weak inhomogeneous Duffin-Schaeffer conjecture is a divergence criterion for almost-everywhere approximation with a fixed additive
shift and unrestricted integer numerators. For a fixed
and a finite-valued function
, it asserts that
 |
implies that, for Lebesgue-almost every 
,
 |
for infinitely many positive integers 
. Here 
is the totient function
and 
is distance to the nearest integer.
The nearest integer 
is not required to be coprime to 
. The exceptional null set may depend on both 
and 
.
