smc

Factor repeatedly with difference of squares. $$2^{48}-1=(2^{24}+1)(2^{12}+1)(2^6+1)(2^6-1)$$ We only care about two terms: $2^6+1$ and $2^6-1$. These simplify to $65$ and $63$. Thus, our answer is $\boxed{63,65}.$