\(a,A=2^{16}-1=\left(2^8-1\right)\left(2^8+1\right)=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ =\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ =3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\\ < 6\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=B\)
\(b,x^2+y^2+z^2+2x-4y+6z+14=0\\ \Leftrightarrow\left(x^2+2x+1\right)+\left(y^2-4y+4\right)+\left(z^2+6z+9\right)=0\\ \Leftrightarrow\left(x+1\right)^2+\left(y-2\right)^2+\left(z+3\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\y=2\\z=-3\end{matrix}\right.\\ \Leftrightarrow P=-1+2-3+2015=2013\)
