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This was a question asked in a competitive exam:

$(300^{3000} -1 )$ is divisible by

a) $401$ b) $501$ c) $301$ d) $901$

The answer is $301$. Not sure how they arrived at the answer. Can somebody explain ?

  • 3
    That it is divisible by 301 can be seen by looking at it mod 301 where it becomes $(-1)^{3000} - 1 = 1- 1 = 0$. That it is not divisible by the other numbers is not as easy to see, but I assume this was not a test where multiple answers could be correct.2012-07-16
  • 0
    300^3000 -1 is in the form x^n -1 which id divisible by x-1 so it is divisible by 300-1 that is 299.2012-07-17
  • 1
    @priti: The question asked which of the following is a divisor of $300^{3000}-1$, your answer - $299$ - does not appear on that list.2012-07-17

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