= Solution
Suppose $Q_1,Q_2$ are <equivalent martingale measures>. Fix a finite maturity $T$ and an event $E\in\mathcal F_T$. Because the market is a <complete market>, replicate the claim $H=B_T\mathbf1_E$, whose discounted payoff is bounded. For a <self-financing strategy>, the discounted value satisfies
$$
\widetilde V_{t+1}-\widetilde V_t=h^S_t(\widetilde S_{t+1}-\widetilde S_t),\qquad\widetilde S=S/B.
$$
Under either pricing measure its conditional mean increment is zero, since $h^S_t$ is known at time $t$ and the discounted stock is a <martingale>. In the standard admissible discrete-time pricing class these finite-horizon values are integrable; a constant lower bound on discounted wealth also gives <integrability> successively from the conditional increment formula. Therefore replication and taking <expectations> give
$$
\frac{V_0}{B_0}=\mathbb E_{Q_j}[H/B_T]=Q_j(E),\qquad j=1,2.
$$
The replicating <portfolio> and its initial cost are the same for both measures, so $Q_1(E)=Q_2(E)$. Since $E$ was arbitrary, the measures agree on $\mathcal F_T$, for every finite $T$, and hence on the <sigma-algebra> generated by the market <filtration>. Thus $\boxed{\text{the equivalent martingale measure is unique}}$. This is the measure version of <complete markets have unique state-price densities>.
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