If there is no upper limit on t, can you find a t such that: e^{iat} = e^{ia_0}, e^{ibt} = e^{ib_0} and e^{ibct} = e^{ic_0} at the same time?
No matter what a,b and c is, though given a != b , a!=c, b!=c and a!= 0, b!= 0, c!=0
Or maybe rather:
at=a_0 +k_12\pi, bt=b_0 +k_22\pi and ct=c_0...