# Prove Addition Exists....Sorta

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• May 13th 2010, 10:10 PM
geekwholuvsdamat
Prove Addition Exists....Sorta
Given $(\mathbb{Z}_n, +)$ and a new element $k$, for what $n$ can $k\cup(\mathbb{Z}_n, +)$ be turned into a ring so that + in $\mathbb{Z}_n$ becomes multiplication in $\mathbb{R}$, $k$ becomes $0_\mathbb{R}$?