Units and Systems of Congruences

1) Make a list of the units in Z16, and with each unit give its multiplicative inverse.

2) Solve the following system of congruences

X=2 (mod 3)
X=3 (mod 5)
X=6 (mod 7)

3) Solve the following system of congruences

X=2 (mod 3)
X=3 (mod 5)
X=4 (mod 7)
X=5 (mod 11)

Any help would be great.

Use Chinese Remainder Theorem for (2),(3).
For (2), your a_1, a_2, a_3 in the above link are 2,3,6, respectively.
Your m_1, m_2, m_3 are 3,5,7 (relative primes).
Your M would be 3*5*7 = 105.

You need to calculate each b's value in the above link and calculate x (Verify your answer is correct).