Problem 27 Proof Recitation

By Joelle Walker

## 27.

## a.

For u, v_{1}, v_{2} ∈ R

Let uv_{1} = 1 and uv_{2} = 1

Then uv_{1} = uv_{2}

uv_{1}v_{1} = v_{1}uv_{2}

And since uv_{1} = 1, then v_{1}=v_{2} 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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