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How many positive integers less than 2000 are of the form x^n for some positive integer x and n≥ 2?

 Sep 4, 2023
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You can find positive integers less than 2000 that can be expressed as x^n for x and n both being positive integers where n ≥ 2, you can break it down as follows:

  1. Start with x = 2, which is the smallest possible base for this problem.
  2. Calculate 2^n for increasing values of n until 2^n exceeds 2000.
  3. Repeat the process for x = 3, 4, and so on, until x^n exceeds 2000 for each x.
  4. Count all the unique values obtained in the process.
 Sep 4, 2023

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