Multiple choice general knowledge math & puzzles

The largest number amongst the following that will perfectly divide 101^100 - 1 is

  1. 100

  2. 1000

  3. 10000

  4. 100^100
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 101^100 - 1, we can write it as (100+1)^100 - 1. Using binomial expansion, all terms except the constant term are multiples of 100, so the expression is divisible by 100. For higher powers of 10, we need to check: 10000 = 10^4 divides it because the binomial expansion includes terms with 10^4 as a factor.

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