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2
questions
5
votes
3
answers
183
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Sanity check on factorization of $\langle 5 \rangle$ in $\mathbb{Z}_{10}$
Looking at $\mathbb{Z}_{10}$, consisting of $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ with addition and multiplication adjusted so the ring is closed under both operations.
Clearly $5 = 3 \times 5 = 5 \times 5 =...
- 1,108
8
votes
5
answers
14k
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Proving gcd($a,b$)lcm($a,b$) = $|ab|$
Let $a$ and $b$ be two integers. Prove that $$ dm = \left|ab\right| ,$$ where $d = \gcd\left(a,b\right)$ and $m = \operatorname{lcm}\left(a,b\right)$.
So I went about by saying that $a = p_1p_2......
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