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July 23rd, 2017, 12:39 PM   #1
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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.
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July 23rd, 2017, 01:13 PM   #2
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Cordiallement non
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July 24th, 2017, 01:57 AM   #3
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Salut,

Cordialement.
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July 24th, 2017, 12:56 PM   #4
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For 2, n=3, k=2.
For 3, a=b=c=1.
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July 24th, 2017, 02:14 PM   #5
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(3). (a, b, c) = (1, 1, 1) or (4, 2, 2)
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July 24th, 2017, 02:21 PM   #6
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Well, at least (2) is solved. https://en.wikipedia.org/wiki/Catalan%27s_conjecture
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