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In the report, we will present a joint discrete universality theorem for the Riemann zeta-function $\zeta(s)$ and Hurwitz zeta-function $\zeta(s,\alpha)$, $s=\sigma+it$, $0<\alpha\leq 1$. Let $D=\left\{s\in \mathbb{C}:\; \tfrac{1}{2}<\sigma<1\right\}$, $\mathcal{K}$ be the class of compact subsets of $D$ with connected complements, $H_0(K)$, $K\in \mathcal{K}$, be the class of non-vanishing continuous functions on $K$ which are analytic in the interior of $K$, and let $H(K)$, $K\in \mathcal{K}$, be the class of continuous functions on $K$ which are analytic in the interior of $K$. Define the set $L(\mathcal{P}, \alpha,h)=\left\{(\log p: p\in \mathcal{P}), (\log(m+\alpha): m\in \mathbb{N}_0), \tfrac{2\pi}{h}\right\}$, where $\mathcal{P}$ is the set of all prime numbers, and $h>0$ is a fixed number.
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{\bf Theorem.} {\it Suppose that the set $L(\mathcal{P},\alpha,h)$ is linearly independent over the field of rational numbers, $K,K_{1}\in\mathcal{K}$, $f(s)\in H_{0}(K)$ and $f_{1}(s)\in H(K)$. Then, for every $\varepsilon>0$,
\begin{eqnarray*}
\liminf_{N\to\infty}\frac{1}{N+1}\# \left\{0\leq k\leq N: \sup_{s\in K}|\zeta(s+ikh)-f(s)|<\varepsilon,\right. \cr\cr\left. \sup_{s\in K_{1}}|\zeta(s+ikh,\alpha)-f_{1}(s)|<\varepsilon\right\}>0.
\end{eqnarray*}
}
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The theorem is a discrete version of the Mishou theorem proved for continuous shifts $\left(\zeta(s+i\tau),\zeta(s+i\tau,\alpha)\right)$ with transcendental $\alpha$.