Chinese Remainder Theorem 1

Problem:

Solve the linear congruence 17x ≡ 3 (mod 2 * 3 * 5 * 7) by solving the system:

a) 17x ≡ 3 (mod 2)
b) 17x ≡ 3 (mod 3)
c) 17x ≡ 3 (mod 5)
d) 17x ≡ 3 (mod 7)

I have been able to solve a), c) and d but I can't solve b. I need all solutions in order to solve the linear congruence. Can anyone help? Thank you!

Quote:

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Originally Posted by jmc1979

b) 17x ≡ 3 (mod 3)

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What is the problem?
Subtract the modulos from the right side,

17x = 3 - 3 =0 (mod 3)
Thus,
17x=0(mod 3)
Divide,
x=0(mod 3)