# Algebraic Integers in a Cyclotomic Field

Let $p >5$ be a prime number. Prove that every algebraic integer of the $p$th cyclotomic field can be represented as a sum of (finitely many) distinct units of the ring of algebraic integers of the field.

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Did you mean to leave off the p > 5 assumption which is in the problem you linked? –  Jason DeVito Aug 24 '10 at 1:35
@Jason: No! I am sorry it was a mistake. –  anonymous Aug 24 '10 at 2:06
Why are you posting deep questions like this when your answers elsewhere [1] make it crystal clear that you don't even understand the most rudimentary number-theoretical concepts such as LCM? [1] math.stackexchange.com/questions/3118 –  Bill Dubuque Aug 24 '10 at 3:17
Let's try to keep our eye on the question and not the questioner. Whether a question is appropriate should depend very little on who is asking it. –  Pete L. Clark Aug 24 '10 at 15:34
@Pete: Please do tell how you propose to explain the answer to such a question to someone who has difficulties with rudimentary number theory concepts. The level of knowledge of the OP is extremely relevant to providing a good answer. –  Bill Dubuque Aug 24 '10 at 23:24

Miklos Schweitzer is a very hard contest.

Anyway, solution for this (and other problems) can be found in the book: