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Consider an arithmetic progression whose first term and common difference are both 100. If the nthn^\text{th}nth term of this progression is equal to 100!100!100!, find n.n.n.
Notation: !!! denotes the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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