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July 23rd, 2017, 12:39 PM  #1 
Member Joined: May 2017 From: France Posts: 57 Thanks: 1  Exponential Diophantine Equations
Hi, Solve : 1/ $\displaystyle n,k\in \mathbb{N}, 29+2^n=3^k$ 2/ $\displaystyle n,k\in \mathbb{N}, 1+2^n=3^k$ 3/ $\displaystyle a,b,c\in \mathbb{N}, 2^a+3^b=5^c$ Cordially. Last edited by skipjack; July 24th, 2017 at 01:58 PM. 
July 23rd, 2017, 01:13 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Cordiallement non 
July 24th, 2017, 01:57 AM  #3 
Member Joined: May 2017 From: France Posts: 57 Thanks: 1 
Salut, Cordialement. 
July 24th, 2017, 12:56 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723 
For 2, n=3, k=2. For 3, a=b=c=1. 
July 24th, 2017, 02:14 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
(3). (a, b, c) = (1, 1, 1) or (4, 2, 2)

July 24th, 2017, 02:21 PM  #6 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328 
Well, at least (2) is solved. https://en.wikipedia.org/wiki/Catalan%27s_conjecture 

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diophantine, equations, exponential 
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