What is the unique three-digit positive integer $x$ satisfying $$100x\equiv 1\pmod{997}~?$$
Question:
What is the unique three-digit positive integer $x$ satisfying $$100x\equiv 1\pmod{997}~?$$
Answer:
Let's think step by step.

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What is the unique three-digit positive integer $x$ satisfying $$100x\equiv 1\pmod{997}~?$$
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