Abstract
Since the pioneering work of Gauss, the cyclotomic problem, viz., the problem of determining cyclotomic numbers of a specific order in terms of solutions of a certain diophantine system, has been treated by many authors. L. E. Dickson laid the foundations of modern cyclotomy when he showed how the Jacobi sums play an important role in this theory. The present paper is a survey of the work of a number of mathematicians on this problem and indicates the current status of the problem. Recently, Paul van Wamelen has obtained a solution to the problem for any modulus.
Dedicated to Prof. A. R. Rajwade
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Katre, S.A. (2002). The Cyclotomic Problem. In: Adhikari, S.D., Katre, S.A., Ramakrishnan, B. (eds) Current Trends in Number Theory. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-09-5_5
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DOI: https://doi.org/10.1007/978-93-86279-09-5_5
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