Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 138, Issue 7, Pages 2283-2288Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-10-10331-1
Keywords
Quadratic residues; Galois field; Chebotarev density theorem.
Categories
Funding
- EP-CONACyT [796853]
- PAPIIT [100508]
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Let S = {a(1),a(2),...,a(l)} be a finite set of non-zero integers. In this paper, we give an exact formula for the degree of the multi-quadratic field Q(root a(1),root a(2),...,root a(l)) over Q. To do this, we compute the relative density of the set of prime numbers p for which all the a(i)'s are simultaneously quadratic residues modulo p in two ways.
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