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Little proof

I'm studying mathematics and I asked myself (by trying to solve another problem) if it could be possible for an integer to be such that its natural logarithm is also an integer. It's true for 1, because 1 is an integer and ln(1) = 0 is an integer. But for strictly positive integer, I couldn't tell.

So I thought a little and came up with that. It's obviously nothing incredible or anything, you probably won't learn anything. I was just happy with that and wanted to try and write it in LaTeX.

Is the proof right ? And if you have advices for using LaTeX or anything, I'll gladly hear them. Thanks for your time !

Here's the link : https://docdro.id/dFeH44o

submitted by /u/xefeer
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from math https://ift.tt/2IZbpOl
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