Problem 27 Proof Recitation

By Joelle Walker

27.

a.

For u, v1, v2 ∈ R
Let uv1 = 1 and uv2 = 1
Then uv1 = uv2
uv1v1 = v1uv2
And since uv1 = 1, then v1=v2 QED.

b.

Assume GCD(a,n) = 1, then ∃ u,v ∈ ℤ such that au + nv =1 → [a][u] + [n][v] = [1] and [n][v]=0 since [n]=[0], so [a][u]=[1] QED.

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