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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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