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November 10th, 2017, 05:23 AM   #1
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exponential equation

$\displaystyle 11^n =11n \; \; $ for $\displaystyle n\in N$
Use Number Theory theorems or approximations
Post your method
(just posting for curiosity); I'll post my idea too.

Last edited by skipjack; November 10th, 2017 at 07:27 AM.
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November 10th, 2017, 07:28 AM   #2
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It seems somewhat obvious that $n$ = 1.
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November 10th, 2017, 08:45 AM   #3
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Re-arrange: 11^(n-1) = n
Still obvious that n=1, as Skip says...
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November 10th, 2017, 08:59 AM   #4
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Math Focus: Wibbly wobbly timey-wimey stuff.
The only other solution is around n = 0.121721. The formula is here, but it's not an integer anyway.

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