Question

Determine all invertible elements of Z [i].
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Answer 1

Answer:

third point:

i) Determine two integers α and β such that 12α+7β=1

Answer: α=3 and β=−5

ii) Determine all the solutions of

7x≡1(mod.12)

Answer: [−5]12={−5+12k,k∈Z}

iii) determine invertible elements (for product) for (Z12,+,⋅), 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]∈Z12 such that [a][6]=[2].

Answer: No, doesn't exist. gcd(6,12)≠1