Questions tagged [diophantine-equations]

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

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Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
1k views

Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$

I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ...
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How to find lattice points on a line segment?

How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers?
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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 ...
190 views

FrobeniusSolve with solutions only being 0 or 1 being acceptable

I want an EFFICIENT way of solving the Frobenius Equation a1 n1 + a2 n2 + a3 n3 + ... + aK nK = U where n1, n2, ..., nK are restricted to be either 0 or 1. I ...
2k views

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 ...
145 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. ...
629 views

Is there a way to use functions like Prime[n] within Solve[]?

I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use Solve[ Prime[n] + Prime[m] == 100, {n, m}] But that ...
165 views

How do I declare a countably infinite list of variables as being integers?

I want to do this, Solve[ { n1 + n2 + n3 + .... = 10, n1 + 2 n2 + 3 n3 + .... = 100}, {n1,n2,n3,....}, Assumptions -> {n1,n2,n3,.... are Integers >=0} ] ...
Solve this equation using Mathematica: $2^x + 113^y = z^2$, $\operatorname{gcd}(x, y) = 1$.