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An Iterated Floor Equation (Posted on 2020-09-15)

Let [x] denote the floor of x.

Then what values of x are solutions to x*[x*[x*[x]]] = 2020?

No Solution Yet Submitted by Brian Smith

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An approach

| Comment 3 of 9 |

[x*[x*[x]]] is an integer, so x is necessarily 2020/k where k is an integer.

Why not just try all integers k in a certain range, instead of iterating to a solution?

The 4th root of 2020 is approximately 6.7.

So I would try all integers between 2020/7 and 2020/6, which is 288 to 336. Also -336 to -288. It seems a lot easier than iterating by .0001.

Posted by Steve Herman on 2020-09-15 18:52:23

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