Consider the theorem:
Theorem:
Let $ \ p_0 \ $ be a fixed prime. Then, for an odd prime $ \ p \ ( \neq p_0 ) \ $ the equation $ \ x^2=p_0 \ (mod \ p) \ $ has a solution if and only if $ \ p=\pm l^2 \ \ (mod \ 4p_0) \ $ when $ \ l \in \{0,........., 4p-1 \} \ $ is odd.
Now use the above theorem to show that if $ \ p_0 \ $ is a fixed prime , then there exists some $ \ a_0 \in \phi(4p_0) \ $ and some $ \ b_0 \in \phi(4p_0) \ $ such that for any prime $ \ p \ $ such that $ \ p =a_0 \ (mod \ 4p_0) \ $ , we have $ \ \left( \frac{p_0}{p} \right) =1 \ $ and for any prime $ \ q \ $ such that $ \ q = b_0 \ (mod \ 4p_0) $ , we have $ \ \left( \frac{p_0}{q} \right) =-1 \ $
Answer:
I am getting no way to hit the question .
Can someone help me