Submission date: 17 May 2014.

Abstract:

We have proved a classical theorem due to Legendre, about the existence of non trivial solutions of quadratic diophantine equations of the form ax^2+by^2+cz^2=0, in the weak fragment of Peano Arithmetic

Mathematics Subject Classification: 03C62

Keywords and phrases:

Full text arXiv 1405.4367: pdf, ps.