Prove that a natural number \(n\) can be represented as a sum of two square if and only if in the prime decomposition: \[n = p_1^{s_1}p_2^{s_2}...p_r^{s_r}\] each prime \(p_f=4k+3\) has an even corresponding power \(s_f\).
In case if \(n= p_1^{s_1}p_2^{s_2}...p_r^{s_r}\) can be represented as a sum of two squares, how many ways are there to do so.