If $a$, $b$, and $c$ are known, is there an efficient way to find values of $x$ which satisfy $x^a\ \textrm{mod}\ b \geq c$ ?
Find $x$ satisfying $x^a\ \textrm{mod}\ b \geq c$ where $a$, $b$, and $c$ are known
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modular-arithmetic
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1Note that $x$ might not exist, e.g., for $c\geq b$. Or it might be not unique... – 2011-04-11