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Exercise: Solve the following system of equations:
1 (mod 4)
0 (mod 3)
Using the explicit formula for a Chinese remainder theorem solution for a system of two equations when the moduli are coprime, we find that the unique congruence class of solutions is:
1 ⋅ (3 ⋅ 3-1) + 0 ⋅ (4 ⋅ 4-1) (mod (4 ⋅ 3))
9 (mod 12)