Let $f_k(x,y,z,t) =2^x+3^y+5^z+7^t, x,y,z,t \in N$, where $k=4$ and defines the number of consecutive primes used for the function, i.e. here: {2,3,5,7}. For all prime $p$ find all such $(x,y,z,t)$ such that $f(x,y,z,t)=p$ (if exists).
Additional question: how does that change when $f_2(x,y)=2^x+3^y$ (and the rest of the task changes accordingly)?