Based on your suggestion, I further modified the method as follows:
In[69]:= Solve[Mod[{1/s, 1/s, 1/s}, 1] == {0, 0, 0}, s,Reals, Assumptions -> Abs[s] >= 1]//RepeatedTiming
Solve[Mod[{1/s, 1/s, 1/s}//Abs, 1] == {0, 0, 0}, s,Integers]//RepeatedTiming
Out[69]= {0.0776961, {{s -> -1}, {s -> 1}}}
Out[70]= {0.458132, {{s -> -1}, {s -> 1}}}
To my surprise, the first method is more efficient.
Regards,
Zhao