Just in case people were not aware, in the case of the single exponential problem $a^{n}=t$, if there is a solution modulo all prime powers, then there is an integer solution. [A nice proof is given in Cojocaru and Murty's book "An introduciton to sieve methods and their applications".

Just in case people were not aware, in the case of the single exponential problem $a^{n}=t$, if there is a solution modulo all prime powers, then there is an integer solution. [A nice proof is given in Cojocaru and Murty's book "An introduction to sieve methods and their applications".