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x^2 = 78 (mod 41503). If a solution exist then find a positive integer that satisfies the solution. Here, = means "congruent to".

I understand the fact that if 78 is the quadratic residue of 41503 then we have a solution but I don't know how I should do that? Should I break down 78 into factors of prime and then try to verify using quadratic reciprocity? Assuming that there IS a solution, how do I find an integer that satisfies the congruent? Please help! thanks!