# Systems of Congruences : Simultaneous Solutions

1. Prove that gcd (a, lcm[b, c]) = lcm[gcd(a,b), gcd(a,c)].

2. Find the simultaneous solutions of the following congruences:

2x ≡ 1(mod 5)

3x ≡ 9 (mod 6)

4x ≡ 1 (mod 7)

5x ≡ 9 (mod 11)

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#### Solution Summary

Simultaneous solutions of congruences are found. The solution is detailed and well presented.

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