Abstract
Under certain conditions, we show the nonexistence of an element γ in the p-th cyclotomic field over ℚ, that satisfies γ γ̄ = n. As applications, we establish the nonexistence of some difference sets and affine difference sets.
Research partially supported by NSA grant MDA 904–90–H-4008 and by an Alexander-von-Humboldt fellowship. The author thanks the Mathematisch es Institut der Universität Giessen for its hospitality during the time of this research.
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Dedicated to Hanfried Lenz on the occasion of his 80th birthday
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© 1996 Kluwer Academic Publishers, Boston
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Arasu, K.T., Pott, A. (1996). Impossibility of a Certain Cyclotomic Equation with Applications to Difference Sets. In: Jungnickel, D. (eds) Designs and Finite Geometries. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1395-3_2
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DOI: https://doi.org/10.1007/978-1-4613-1395-3_2
Publisher Name: Springer, Boston, MA
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