Diophantine equation where the variable is in the exponent (ex.: find all sols for $3^x-5^y=7$)
Diophantine equation where the variable is in the exponent (ex.: find all sols for $3^x-5^y=7$)
Questions tagged [exponential-diophantine-equations]
101 questions
2
votes
2 answers
Solve the Diophantine equation $ (3^{n}-1)(3^{m}-1)=x^{r} $
Is there a solution other than solution
\begin{equation*}
(3^{2}-1)(3^{2}-1)=2^{6}=4^{3}
\end{equation*}
of the Diophantine equation
\begin{equation*}
(3^{n}-1)(3^{m}-1)=x^{r}
\end{equation*}
for positive integers $ n, m, x, r $ such as $ n, m, x…
1
vote
0 answers
Proving no more solutions for Diophantine equation
Equation
$$a^2=2^n-k$$
$$a,n,k>1 \quad \text{and} \quad k
oddy
- 51
1
vote
0 answers
Integer solution of $2 m (2^{n+1} - 1) = n (3^{m+1} - 1)$
I was reading a lot of other questions here which are supposed to be similar, but none of the answers gave me a hint, how I can approach this. I wrote a Python program to solve it, but up to $2^n < 1e20$ there were no solutions. So I guess my…
Rüdi Jehn
- 594
0
votes
1 answer
Are there non-trivial integer solutions for $3^x=2^y+1$?
Consider the equation: $3^x = 2^y+1$
(with $(x,y) \in \mathbb{N}^2$)
There are two easy to find solutions ((1,1) and (2,3)), but it doesn't look like there are more of them.
Are there more solutions to this equation?
Anne Aunyme
- 382
0
votes
0 answers
Determine the natural numbers $x$, $y$ such that $3 \cdot 2^x+1= 7^y$
Determine the natural numbers $x$, $y$ such that $3\cdot 2^x+1= 7^y$.
I have some not-really-good ideas we can start with:
Using the last figure and determine the parity of the number and many more divided.
I don't know why I thought of it, but we…
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