In the RSA algorithm, what property of the modulus helps ensure the algorithm's correctness?

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In the RSA algorithm, what property of the modulus<br><img src='https://www.fatskills.com/images2/GradExams/87C18D5A-D56A-4321-AED2-0CE9E5D3FA68.png' height='10' width='17'/> helps ensure the algorithm's correctness?