2-universal positive definite integral quinary diagonal quadratic forms
The authors determine all positive definite integral quinary diagonal quadratic forms that are 2-universal, i.e. that represent all positive definite integral binary quadratic forms. These are the forms: \(\langle 1,1,1,1,1 \rangle\), \(\langle 1,1,1,1,2 \rangle\), \(\langle 1,1,1,1,3\rangle\), \(\langle 1,1,1,2,2\rangle\), \(\langle 1,1,1,2,3\rangle\). It was already shown by \textit{M. Peters} [Acta Arith. 24, 157-164 (1973; Zbl 0258.12001)] (see Lemma p. 158) that these five forms are 2-universal.
positive definite integral quinary diagonal quadratic forms
scientific article; zbMATH DE number 1185659