科研之友
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摘要
Let K-n = Q(zeta(n)) be the n-th cyclotomic field with n not equivalent to Z (mod 4). Let O-n = Z[zeta(n)] be the ring of integers of K-n and S-n the set of all elements alpha epsilon O-n which are sums of squares in On. Let gn be the smallest positive integer in such that every element in S-n, is a sum of m squares in O-n. In this Note, we show that g(n) = 3 unless n is odd and the order of 2 in (Z/nZ)* is odd, in which case g(n) = 4.
