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Exercise: Solve the following system of equations:
x
1 (mod 8)
x
4 (mod 9)
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:
x
1 ⋅ (9 ⋅ 9-1) + 4 ⋅ (8 ⋅ 8-1) (mod (8 ⋅ 9))
49 (mod 72)