Abstract
For integers m ≥ 2 and d ≥ 1, we study the set S m of m consecutive integers which satisfies the property that for each x ∈ S m there exists y ∈ S m such that gcd(x, y) > d. This problem was first posed and studied by S. S. Pillai for the case d = 1. In this article, we elaborate on an argument of T. Vijayaraghavan for d = 1 and of Y. Caro for d ≥ 1.
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Saradha, N., Thangadurai, R. (2009). Pillai’s Problem on Consecutive Integers. In: Adhikari, S.D., Ramakrishnan, B. (eds) Number Theory and Applications. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-46-0_13
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DOI: https://doi.org/10.1007/978-93-86279-46-0_13
Publisher Name: Hindustan Book Agency, Gurgaon
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