Consider a non-empty set of positive integers M. We know, that when some x is in M, then so are 4x and [sqrt(x)].
Determine all integers in M.
Note: For a real number x, [x] denotes the largest integer, that is smaller or equal to x.
Not a proof but:
Given any x in M, successive square roots of x will be in M, and these will tend to the value 1.
Having 1 in M and considering that 4 times any member of M is also in M would I think then garantee M would include all positive integers?
Tried this iteratively for a while and eventually all positive integers up to 20 were included along with a lot of other seed values that would continue adding to M.
Someone with more skills needed!
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Posted by Kenny M
on 2020-01-19 10:46:16 |
Possibly
