removed tag 'representation'; edited question for clarity and correctness; changed 'modulus' back to 'absolute value'

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edited Mar 2, 2015 at 23:58

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When does the modulusabsolute value of a sum of an integer and an algebraic integer equal an integer?

LetLet's say Z is a sum of n-rootsth roots of unity and thus an algebraic integer, and D is ana rational integer. If |z+D| If |z+D| is an integer, what can we conclude regarding Z? canCan we say |Z| is an integer? Another related question is, for: For which non-zero D, we can we conclude that |Z| is an integer from the given thatif |Z+D| is an integer?