If I have k algebraic integers like a_1, ..., a_k such that the sum of their n-power are integer for n=1, ...m can we deduce that a_1, ..., a_k are integers? how large m should be? (how many power sum should be integers to deduce all a_i's are integers)
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
0
|
|||||||||
|
closed as too localized by Gjergji Zaimi, Andreas Blass, Andres Caicedo, Qiaochu Yuan, Dan Petersen Oct 25 at 6:27 |
|
3
|
A common theme to all comments and answers prior to this is the fact that if the algebraic integers you start with are closed under algebraic conjugation, then the power sums are all necessarily (by Galois theory) rational, so they are always (rational) integers, as rational algebraic integers are integers. |
||
|
|
You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.
|
2
|
Take any monic polynomial with integer coefficients and look at the roots. |
||
|
|
