We consider IOpen, the subsystem of Peano Arithmetic with the induction scheme restricted to quantifier-free formulas. We prove that each model of IOpen can be embedded in a model where the equation x 1  2 +x 2  2 +x 3  2 +x 42 =a has a solution. The main lemma states that there is no polynomial f(x, y) with coefficients in a (nonstandard) DOR M such that |f(x, y)| 0 is a nonstandard element of M
['Margarita Otero']
On Diophantine equations solvable in models of open induction