# Questions tagged [linear-diophantine-equations]

Diophantine equations where all of the terms are monomials of degree zero or one. For example, finding all integers $x$ satisfying $ax = b$, finding all integers $x,y$ such that $ax + by = c$, or finding all integers $x,y,z$ such that $ax + by + cz = d$. Probably appropriate with (elementary-number-theory).

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### A man cashes a check for $d$ dollars and $c$ cents [duplicate]

I know this question has been asked before, but the answer to the previously posted question does not address my question about the problem. I will restate the problem: A man cashes a check for $d$ ...
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### A man buys a dozen pieces of fruit...Questions about finding which solutions work [duplicate]

From Dudley's Elementary Number Theory, Section 3 on Linear Diophantine Equations, he poses the problem "A man bought a dozen pieces of fruit--apples and oranges--for 99 cents. If an apple costs ...
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### When formulating the general solutions to a linear diophantine equation $ax + by = c$, does it matter which term is $x$ and which is $y$?

I saw the problem I am working on posted some years ago, and I cannot see how changing the order of the terms can matter, but when applying the general solution after finding one solution, my ...
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### Solving linear diophantine equations - methods and complexity

I'm curious what (if any) are the state-of-the-art methods to find solutions for linear diophantine* equations of N variables, like: $$\sum _{i=1} ^{n} a_{i}x_i ~=~ b$$ Note that I mean a single ...
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### Solving equation to get all possible solutions [duplicate]

This is a question on entrance exam. It says for positive integers $x,y,n,k$ and $n,k>1$ find all the possible solutions to $20x^k+24y^n =2024$ I found a wrong solution when $x^k =100$ so $x$ can ...
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### Diophantine equations - is my reasoning valid here?

I was thinking about the Diophantine equation $20x+24y=2024$ for a class today. There is an obvious solution: $x=100,y=1$ but there are other solutions as well where $x$ and $y$ are both positive ...
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### Is there a way to find the values of 3 variables with just one equation?

I was doing a personal project until I came upon this equation that i need to solve to continue, the thing is I don’t thing I have been thought this in math ever so i wonder if this even possible to ...
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### minimum solutions for linear Diophantine equation in n variables

As we know for the most simple Diophantine equation $ax+by=1$ for positive $a,b$ if $1\le x\le b-1$ then $-(a-1)\le y\le -1$ but what if we have n variables and not just two , if equation be equals to ...
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