digits 100
pOf2=vpa(2);
for x=2:300
    pOf2=pOf2*2;
    p4=pOf2+17;
    root4=round(p4^(1/4));
    if root4*root4*root4*root4==p4
       disp([x root4])
    end
end

Finds only x=6, y=3.