# Almost 2-universal diagonal quinary quadratic forms

## TL;DR

This paper proves that three specific quinary diagonal quadratic forms are almost 2-universal, meaning they represent all but finitely many binary quadratic forms, advancing the classification of such forms.

## Contribution

It confirms that the three remaining candidate forms are indeed almost 2-universal, completing their classification.

## Key findings

- All three candidate forms are proven to be almost 2-universal.
- The classification of almost 2-universal quinary diagonal quadratic forms is completed.
- The results refine understanding of representation properties of quadratic forms.

## Abstract

A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms except those in only finitely many equivalence classes. Oh [7] determined all almost 2-universal quinary diagonal quadratic forms remaining three as candidates. In this article, we prove that those three candidates are indeed almost 2-universal.