Let's say Z is a sum of n-th roots of unity and thus an algebraic integer, and D is a rational integer. If |z+D| is an integer, what can we conclude regarding Z? Can we say |Z| is an integer? Another related question is: For which non-zero D can we conclude that |Z| is an integer if |Z+D| is an integer?
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removed tag 'representation'; edited question for clarity and correctness; changed 'modulus' back to 'absolute value'
Ricardo Andrade
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When does the absolute value of a sum of an integer and an algebraic integer equal an integer?
katie
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