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 November 10th, 2017, 05:23 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 634 Thanks: 91 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.
 November 10th, 2017, 07:28 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 It seems somewhat obvious that $n$ = 1. Thanks from topsquark
 November 10th, 2017, 08:45 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re-arrange: 11^(n-1) = n Still obvious that n=1, as Skip says... Thanks from topsquark
 November 10th, 2017, 08:59 AM #4 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,266 Thanks: 934 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. -Dan

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