Find 100 consecutive natural numbers, each of which is composite
So this is the sort of quesition where you will spend a while thinking about it, probably feel a little silly you haven't gotten it yet, then go "aha!", write down the answer and move on. It's all about spotting the trick.
Here the trick is to consider 101!, this is a number that is divisible by 2,3,...,100,101. So our list of 100 consecutive numbers is:
101! + 2,101! +3,...101!+100,101!+101
This works as each 101! + k is divisible by k as 101! and k both are.
GV
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