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I have this excercise, I need your help on the third point:

i) Determine two integers $\alpha$ and $\beta$ such that $12\alpha + 7\beta = 1$

Answer: $\alpha = 3$ and $\beta = -5$

ii) Determine all the solutions of $$7x\equiv 1 (mod. 12)$$

Answer: $[-5]_{12} = \{-5+12k, k\in\mathbb{Z}\}$

iii) determine invertible elements (for product) for $(\mathbb{Z}_{12}, +, \cdot)$, and zero divisors

Answer: Here I need your help! How can I determine all invertible elements and all zero divisors?

iv) determine, if exists, a class $[a]\in\mathbb{Z}_{12}$ such that $[a][6]=[2].$

Answer: No, doesn't exist. $gcd(6,12)\neq 1$

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    I have to pass the algebra exam. Successively i will try to improve that number. :)2012-03-07

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