Yeah, it is still okay. It does not give real (non-trivial) solution, but it still has non-trivial p-adic solution. Maybe I should state more precisely what is a Z_p solution. (or p-adic solution) For example, fix p = 5, suppose I want to solve x^2 + 1 = 0 Then, I first consider mod 5, this gives: x = 2 is a solution, set a_0 = 2. Then I need to find a_1 such that a_1^2 + 1 = 0 (mod 25), and a_1 = a_1 = 2 (mod 5). After that, find a_3 such that a_3^2 + 1 = 0 (mod 5^3) and a_3 = a_2 mod (25), and so on. Then y = a_0 + a_1(5) + a_2(5^2) + …. is a non-trivial 5-adic solution to: x^2 + 1 = 0. (provided that not all a_i = 0 (mod 5). Is this more clear? I am sorry if the question originally stated is ambiguous.

As the first step, can you first show that the equation has non-trivial solution mod p? (for any choice of a_i)