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The question as currently worded, and considering comments by its author, would boil down to: is it a hard problem finding $g^a\bmod p$, given large prime $p$ large integer $g$ less than $p$ that is a generator of $\mathbb Z_p$ [see note 1] prime $r$ less than $p$ knowledge that unknown $a$ is a positive integer less than $r$ positive integer $b$ less than ...


Not at all. It's very trivial: $$(g^{ab})^{b^{-1}}=g^a$$

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