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I1.4 Find the least positive integer $d$, such that $d^{c}+1000$ is divisible by $10+c$.

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Official solution

$\begin{array}{l}d^{3}+1000 \text { is divisible by } 13 \\ 13 \times 77=1001=1000+1^{3} \\ d=1\end{array}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.