A Theorem of Legendre in $I\Delta_0+\Omega_1$

Michele Bovenzi; Paola D'Aquino

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arXiv · 1405.4367

A Theorem of Legendre in $I\Delta_0+\Omega_1$

Michele Bovenzi·Paola D'Aquino

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Abstract

We prove 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 $I\Delta_0+\Omega_1$.

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Michele Bovenzi, Paola D'Aquino. 2014-05-17. A Theorem of Legendre in $I\Delta_0+\Omega_1$. https://arxiv.org/abs/1405.4367

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