  We are concerned on the study of the unique continuation type property for
the 3D incompressible Euler equations in the self-similar type form. Discretely
self-similar solution is a generalized notion of the self-similar solution,
which is equivalent to a time periodic solution of the time dependent
self-similar Euler equations. We prove the unique continuation type theorem for
the discretely self-similar solutions to the Euler equations in $\Bbb R^3$.
More specifically, we suppose there exists an open set $G\subset \Bbb R^3$
containing the origin such that the velocity field $V\in C_s^1C^{2}_y (\Bbb
R^{3+1})$ vanishes on $G\times (0, S_0)$, where $S_0 > 0$ is the temporal
period for $V(y,s)$. Then, we show $V(y,s)=0$ for all $(y,s)\in \Bbb R^{3+1}$.
Similar property also holds for the inviscid magnetohydrodynamic system
