If `10^m` divides the number `101^(100)-1` then, find the greatest value of `mdot`

Explanation

We have , ` 101^(100) - 1 = (1 + 100)^(100) - 1`
` = 1 + ""^(100)C_(1) . 100 + ""^(100)C_(2) . 100^(2) + … + ""^(100)C_(100) 100^(100) -1`
` = ""^(100)C_(1). ""^(100)C_(2). 100^(2) + …+ ""^(100)C_(100). 10^(100)`
` = (100)(1000) + ""^(100)C_(2) . 100^(2) + ... + ""^(100)C_(100) . 100^(100)`
` (100)^(2) [ 1 + ""^(100)C_(2) + ...+ 100^(98)]`
` 100^(2) k `, where k is a positive integer
Therefore , `101^(100) - 1` divisible by `100^(2) i.e., 10^(4)`
` therefore n = 4 `