Let Tn = 1n + 2n + 3n + 4n. Find the number of values of n among first 100 positive integers such that Tn is divisible by 5.

  1. 48
  2. 50
  3. 67
  4. 75

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  1. 75
    Only when n is of the form 4k+4, it will not be divisible by 5. (Using cyclicity to add the unit’s digit)

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