Linked Questions

2 votes
1 answer

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 ...
Leo's user avatar
  • 212
17 votes
6 answers

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 $7^3-3^5=100$.
math110's user avatar
  • 92.5k
5 votes
1 answer

Exponential Diophantine equation $7^y + 2 = 3^x$ [closed]

Find all positive integer solutions to $$7^y + 2 = 3^x.$$ ATTENTION: MY SOLUTION HAS A TERRIBLE MISTAKE WHICH I HAVE OVERLOOKED! Obviously, $x > y$. Then, we have $3^x = 7^y + 2 \equiv 0 \pmod {3^...
user avatar
7 votes
2 answers

Solve $13^x-3^y=10$ in positive integers

As it is "well-known" fact $13-3=10$. Is this true for some other powers of $13$ and $3$, i.e. find all natural numbers $x$ and $y$, such that $13^x-3^y=10$ (there are other, find them all).
Stoyan Apostolov's user avatar
4 votes
2 answers

Solve for integer $m,n$: $2^m = 3^n + 5$

Solve for integer $m$ and $n:$ $$2^m = 3^n + 5$$ My Attempt: Easy to guess two solutions namely $(3,1)$ and $(5,3)$. Also easy to see that a solution will exist iff $m > 0$ and $n > 0$. ...
Anon's user avatar
  • 2,410
3 votes
2 answers

Find positive integer $x,y$ such that $7^{x}-3^{y}=4$

Find all positive integers $x,y$ such that $7^{x}-3^{y}=4$. It is the problem I think it can be solve using theory of congruency. But I can't process somebody please help me . Thank you
Sufaid Saleel's user avatar
1 vote
4 answers

For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.

Problem: For what pair of positive integers $(a,b)$ is $3^a + 7^b$ a perfect square. First obviously $(1,0)$ works since $4$ is a perfect square, $(0,0)$ does not work, and $(0,1)$ does not work, so ...
IntegrateThis's user avatar
2 votes
2 answers

Solve this equation $12^x-5^y=19$ positive integers

Find all $x,y$ be positive integers,such $$12^x-5^y=19$$ I found $(x,y)=(2,3)$ is solution,maybe have other,so I consider case $x,y>3$ and $\pmod 9$,since $$12^x\equiv 0\pmod 9,x\ge 2$$ then $5^y\...
math110's user avatar
  • 92.5k
-2 votes
2 answers

Diophantine equation $2^x-3^y=2021$ [closed]

$$2^x-3^y=2021$$ where $x,y$ are non-negative integers. I only found $2^{11}-3^3=2021$.
spock's user avatar
  • 103
2 votes
5 answers

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.
Theory Nombre's user avatar
-1 votes
1 answer

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?
Raafz Morelli's user avatar
2 votes
3 answers

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 $k$...
MathFanatics's user avatar
8 votes
1 answer

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 ...
Hubert Schölnast's user avatar