ABOUT MORDELL`S DESCENT METHOD

Abstract

In this paper, a complete version of the descent method proposed by Mordell for finding the smallest solutions to Legendre's equation is described. The proofs given are for the Legendre equation arbitrary and without making transformations to bring the equation to the normal form, as has been done so far. Holzer's theorem and Wlliams' corollary can be obtained from the proved theorem,
taking into account the corresponding equivalent equations.