# Questions tagged [diophantine-equations]

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

75 questions
Filter by
Sorted by
Tagged with
149 views

• 1,851
212 views

### One more solution of the Mordell equation

Please, help to find one more solution of the Mordell equation $y^2=x^3+n,\quad n\in\mathbb{Z}$ $$y^2=x^3-307$$ Using Solve I was able to go up to ...
• 16.3k
387 views

### Calculating the integral points of an elliptic curve

I asked this question on Math stachexchange. The question I have is: Can I use Mathematica to find the (integral points on the following elliptic curve) or can I find when the number $\text{n}$ is a ...
• 1,765
1 vote
118 views

• 8,668
417 views

### Solving a diophantine equation with three variables

Solve this equation using Mathematica: $2^x + 113^y = z^2$, $\operatorname{gcd}(x, y) = 1$.
208 views

### Unexpected behaviour with FindInstance

Evaluating FindInstance[a/(b + c) + b/(a + c) + c/(a + b) == 4, {a, b, c}, Integers] does what I'd expect it to do: find a solution to the equation in integers. ...
• 412
224 views

### Storing Multiple solutions from Solve as rows of a matrix

I am trying to find all the solutions to a Diophantine equation (only integer valued solutions) using Solve[], however there are multiple and even many solutions sometimes. How can I store these ...
1 vote
555 views

### determine the coefficients of a quadratic equation with "Solve"

Assume we want to determine the coefficients (integer) of a quadratic equation by having some information about the input and output values. If I enter the input and output individually before the ...
• 808
619 views

### Solving a Diophantine equation with a large solution

I am trying to solve the following Diophantine equation with Mathematica: $\frac{x}{y+z}+\frac{z}{x+y}+\frac{y}{x+z}=4$ It is known that there are three positive numbers that satisfy the equation ...
• 181