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MR808019 11T21 (11D09)
Katre, S. A.; Rajwade, A. R. Complete solution of the cyclotomic problem in ${\bf F}_q$ for any prime modulus $l,\;q=p^\alpha,\;p\equiv 1\;({\rm mod}\,l)$. Acta Arith. 45 (1985), no. 3, 183–199.
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