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### Find all integer solutions of $3^a +7 = 2^b$ [duplicate]

I want to find all integer solutions of $3^a + 7 = 2^b$ I have found (by brute force) the two solutions $3^0 + 7 = 2^3$ and $3^2 + 7 = 2^4$ but I want to see if there are more solutions. I have ...
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### Finding solutions to the diophantine equation $7^a=3^b+100$

Find the positive integer solutions of the diophantine equation $$7^a-3^b=100.$$ So far, I only found this group $7^3-3^5=100$.
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### Diophantine equation $2^x-3^y=2021$ [closed]

$$2^x-3^y=2021$$ where $x,y$ are non-negative integers. I only found $2^{11}-3^3=2021$.
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### The diophantine equation $5\times 2^{x-4}=3^y-1$

I have this question: can we deduce directly using the Catalan conjecture that the equation $$5\times 2^{x-4}-3^y=-1$$ has or no solutions, or I must look for a method to solve it. Thank you.
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### Equation in integers $7^x-3^y=4$

I don't know how to solve $7^x-3^y=4$... I tried to see something $\pmod 7$ and $\pmod 3$ but it doesn't help at all. Can anyone give me some hints about it?
### Find all integer numbers $k$,$l$,$m$,$n$ for which $3^k$ • $5^l$ + $7^m$ = $2^n$
Find all integer numbers $k$,$l$,$m$,$n$ for which $3^k\cdot 5^l+7^m=2^n$. I tried to find a decent modulo and look at ending digits, but nothing more. Thank you for your responses. Obviously is $k$...
### Solutions for diophantine equation $3^a+n=2^b$
A few days ago I asked for a solution for $3^a+1=2^b$ where $a\in \Bbb N$ and $b\in \Bbb N$ (Solutions for diophantine equation $3^a+1=2^b$), and I got two good answers for this question. But there I ...