# Tagged Questions

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

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### Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
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### equidistant solutions in Sequence Sums That Are Squares

In my demonstration "Sequence Sums That Are Squares" I demonstrate two "lines" of solutions (of infinite length) and ask whether someone can find one more line. I am looking forward to your solution. ...
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### Problem on Consecutive Sequence Sums that are Squares

Here is a seemingly simple Problem: I have two natural numbers n and m, n < m such that S1:= n +...+ m is a square and also S2:= n +...+ m + (m+1) is a square. Problem a) : Find n and m. You ...
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### find the number of integral solutions a+b+c+d+e+f = 18 [duplicate]

Find the number of integral solutions of a + b + c + d + e + f = 18 where a, b, c, d, e, f are elements of the range ...
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### Efficient way to solve equal sums $x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k$ with Mathematica?

I need to solve the system of equations, call it $S_1$, in the integers $$x_1x_2x_3x_4x_5 = y_1y_2y_3y_4y_5$$ $$x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k,\;\; k= 2,4,6$$ I used a very ...
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### How to solve this equation with integers as a solution?

I want to solve the equation $$x^y + y = y^x + x$$ with $x$, $y$ are integer numbers. I tried Solve[x^y + y == y^x + x, {x, y}, Integers] How to solve the ...
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### How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?

Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below: ...
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### Extracting Reduce results

I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer. For example, if my input ...
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### Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
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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/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 ...