The ring of finite algebraic numbers and its application to the law of decomposition of primes (Q6585668)

Let \(L\) be a finite Galois extension of \(\mathbb Q\), and let \(\mathrm{Spl}(L)\) be the set of rational primes that split completely in \(L\). For example, for \(K={\mathbb Q}(\sqrt{5})\) one has \(p \in\mathrm{Spl}(L)\) if and only if \(p \equiv \pm 1 \pmod 5\). The authors are interested if there is a rule which for every prime \(p\) determines if \(p\) is in \(\mathrm{Spl}(L)\) or not. They give some results indicating that the set \(\mathrm{Spl}(L)\) can be characterized by the values of a linear recurrent sequence modulo primes and compare their result with some previous results of this type. Some explicit examples are also given.