Inteiros que se escrevem na forma x2 + qy2 , q = 1, 2, 3, ... - Assis, Ricardo de Jesus Caldas (2015)
In this work we are interested in the integers n that are written in the formx2 + 2y2 and x2 + 3y2 . This problem was proposed by Fermat in 1654. The proof of thetheorem about the integers that are written as the sum of two squares x2 + y2can beadapted in order to determine the integers that can be writing in the forms x2 + 2y2 andx2 + 3y2. In this case, we need to use the theorem of unique factorization on the product of primes for numbers of the form a + b√−2; a + bξ3 ξ3 =−1+√−32 ,together with some topics of Number Fields.