González Gascón, FranciscoRamos, F.B.Aguirre Dabán, Eduardo2023-06-212023-06-2119821089-7658http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306https://hdl.handle.net/20.500.14352/64795It is shown that any first integral of type P2()—a polynomial of degree 2 in —of the differential equation =Vx can be obtained from a pointlike gauge symmetry of the action AL associated to L= 1/2 2+V(t,x). The same result holds for any first integral of kind Pn() when dynamical symmetries of AL polynomials in are allowed. The neccessary and sufficient conditions that V(t,x) must satisfy in order that =Vx possesses a first integral of type Pn() have been obtained. These conditions reduce (when n=2) to a condition obtained by Leach. The computational advantages and difficulties which appear in order to obtain first integrals for type Pn() are also briefly discussedjournal articlehttp://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306http://aip.org/metadata only access517.9Partial differential equationspolynomialslangragian functiongauge invarianceEcuaciones diferenciales1202.07 Ecuaciones en Diferencias