A Theorem of Legendre in $IΔ_0+Ω_1$
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 $IΔ_0+Ω_1$.
math.LO↗