Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r = r_1 + r_2 - 1. Then the multiplicative group of units U_K of K has the form U_K = {ζ_K^(e_0) ϵ_1^(e_1) ϵ_2^(e_2) ...ϵ_r^(e_r) :e_i element Z},
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