# Questions tagged [diophantine-equations]

Questions on the use of Mathematica to find integer/rational solutions to equations.

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### how to solve a quadratic diophanic equation on integers and obtain various results

This quadratic di equation has more results, as it came to them. I can only think of this FindInstance[(4 p + 3 q - 2) (p - 1) == (6 p + 2 q) q, {p, q}, Integers] ...
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### 7X7 matrix of distinct cubed integers with identical row and column sums

Problem: find a 7X7 matrix of distinct cubed integers with identical row and column sums. Well, I have the following code (that came from @kglr from my previous question): ...
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### Solving a system of equations using the data generated by PowersRepresentations and ParallelTable

First of all, it is possible to check the code that I am asking for because I know that $x=3051$ must yield at least a solution to the problem. Well, I have the following system of equations: Now, I ...
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### Solving a system of two equations of cube integers using ParallelTable

Well, I have the following problem: I need to solve the following system of equations: $$\begin{cases} n=a^3+b^3+c^3\\ \\ n=d^3+k^3+f^3 \end{cases}\tag1$$ Where: $n\ne a\ne b\ne c\ne d\ne k\ne f$;...
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### How to test solvability of a Diophantine equation?

When applying the BRC theorem I need to test if an equation has a non-zero solution in integers. The equation is of form: $$x^2 + by^2 + cz^2 = 0$$ We could try to directly check if this equation ...
267 views

### Integer partitions without repetitions

What combination of numbers makes a specific sum? The code below is not very effective, because it also gives answers in which a number is used more than once even though it was given in the list ...
131 views

### Finding all solutions in the Roth's theorem

Roth's theorem. For all algebraic irrational $\alpha$ $$\displaystyle \left \lvert \alpha - \frac{p}{q} \right \rvert < \frac{1}{q^{2 + \epsilon}}$$ with $\epsilon>0$, has finitely many ...
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### Puzzle — 20 People to consume 20 units of food under constraints

I am learning Mathematica because I love it. I also love solving puzzles so I think it would be a nice way to learn Mathematica through puzzles. This is first puzzle in series I intend to solve. So ...