We consider IOpen, the subsystem of PA (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 $x^2_1 + x^2_2 + x^2_3 + x^2_4 = a$ has a solution. The main lemma states that there is no polynomial $f(x,y)$ with coefficients in a (nonstandard) DOR $M$ such that $|f(x,y)| < 1$ for every $(x,y) \in C$, where $C$ is the curve defined on the real closure of $M$ by $C: x^2 + y^2 = a$ and $a > 0$ is a nonstandard element of $M$.