/sci/ - Science & Math

Help me out guys. As far as I understand, the last use of Euler's formula in pic related near the end also relies on the fact that we assumed [math]\text{gcd}(c, pq) = 1[/math] at the beginning of the proof. How would I prove the uniqueness of the solution in the case where [math]\text{gcd}(c, pq) \neq 1[/math]?