Rational numbers whose sum and product are both integers

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918, Iran.

Abstract

For $n>2$, there are noninteger rational numbers $r_i, \ i=1, 2, \ldots, n$ such that $\sum_{i=1} ^n r_i$ and $\prod_{i=1} ^n r_i$ are both integers. In this paper, while proving this proposition and with the help of the fundamental theorem of arithmetic and the properties of prime numbers, we will present an algorithm to generate numbers with this feature. Finally, we present a modified version of the original problem that requires further exploration.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 25 October 2025

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