TWO QUESTIONS ON LEVESQUE'S CYCLOTOMIC UNIT INDEX

C.Levesque raised two questions on the index of his independent cyelotomic unitsystem in the whole unit group of Zζ_n+ζ_n].In this paper it is shown that the firstquestion has affirmative answer for n=p~αand n=p~αq~β,the second question has affirmativeanswer for n=p~α,but has negative answer for n=p~αq~β

Two Questions on Levesque's Cyclotomic Unit Index

C. Levesque^3] raised two questions on the index of his independent cyclotomic unit system in the whole unit group of $Z\xi_n +\bar \xi_n\]$.In this paper it is shown that the first question has affirmative answer for n\equiv p^\alpha and n\equiv p^\alpha q^\beta, tho second question has affirmative answer for n\equiv p^\alpha, but has negative answer for n\equiv p^\alpha q^\beta.