No pen and paper. Just think
Number Theory
Level
4
Find the largest integer such that it is divisible by all natural numbers less than its square root.
This is part of the set My Problems and THRILLER
The answer is 24.
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(This is definitely not a solution, yet an idea. Please check out if this idea works. And I'm sorry if this is confusing.)
If we can prove that [[...[[2,3],4]...],x] > (x+1)^2 - 1 for x > 4 then we can be sure that x < 4 or x = 4
If [[...[[2,3],4]...],x] < (x+1)^2 - 1 then we can conclude that there exists at least a number from [[...[[2,3],4]...],x] to (x+1)^2 - 1 so that it is divisible by all natural numbers from 1 to x.
[a,b] is the same as LCM [a,b] by the way.
@Brian Charlesworth Any ideas, sir?