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Concatenate

Author: mathforces
Problem has been solved: 14 times

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Let $X_k$ be a number obtained from the numbers $2^{10}, 2^{20}, …, 2^{10k}$ written in decimal notation by concatenating them together in the specified order. Find the smallest value of $k \geq 3$ such that $X_k \equiv 2^{10k}\ (\text{mod} \ 2^{170})$.





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