A few conjectures about the multiple zeta values

The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper we will show partial solutions to five well known conjectures about the MZV which we partially proved using just linear systems and shuffles products. We saw that to partially solve four of this conjectures we only need linear algebra.