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The first problem in Diophantus' "Arithmetica" involves finding two numbers whose sum is a specific value and whose product is another specific value. This leads to the formulation of a quadratic equation, which represents the relationship between the two numbers. Diophantus seeks integer solutions to this equation, laying the groundwork for what would later be known as Diophantine equations. This problem exemplifies his focus on solving equations with positive rational numbers.

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