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How can I align bullet pointed examples within one example in the amsthm environment?

I am using amsthm to label examples. Rather than have each subsequent example separately, I would like to bullet point multiple examples within one labelled "example." So for instance, I might have 4+3 = 7, 2+4 = 6 and 3+1 = 4 all listed on separate lines with their own bullet point, but all three bullets within example 1.1.

How can I do this? Here is a minimal working example of code, where for the second example I have managed to get the desired result, but have failed for the first example:

\documentclass{article}\usepackage{amsmath, amsfonts,  amssymb, amsthm, bm, graphicx,color} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example}\newtheorem{remark}[theorem]{Remark}\parskip 5mm\parindent 1cm\begin{document}\begin{example}\begin{align*}\text{\textbullet} && & 13 \oplus 3  =  3  \\\text{\textbullet} && & -4 \oplus 15  =  -4  \\\end{align*}\end{example}\begin{example}\begin{align*}         \text{\textbullet} && &\text{For } p = 2, \text{the p-adic (here 2-adic) valuation on } \frac{4}{9} \text{ is } 2, \text{ since } \frac{4}{9} = 2^{2} \cdot \frac{1}{9}, \\&& &\text{where } 2 \nmid 1 \text{ and } 2 \nmid 9.\\    \text{\textbullet} && &\text{For } p = 5, \text{the 5-adic valuation on } \frac{16}{125} \text{ is } -3, \text{ since } \frac{16}{125} = 5^{-3} \cdot \frac{16}{1}, \\&& &\text{where } 5 \nmid 16 \text{ and } 5 \nmid 1.\\\end{align*}\end{example}\end{document}

I have two questions. How do I replicate this second, working example 0.2 for any generic set of examples?Secondly, is there a more efficient way to do this?


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