Questions on the use of Mathematica to find integer/rational solutions to equations.
Questions tagged [diophantine-equations]
92 questions
10
votes
3 answers
How can I select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers?
I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = (5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried
ClearAll[a, b, r, c];
a = 1;
b = 3;
c = 5;
r = 5* Sqrt[3]; ss =
…
Laurenso
- 1,032
- 2
- 11
9
votes
3 answers
How can I get all squares on this sphere so that its coordinates are integer numbers?
I have the sphere (x-2)^2 + (y-4)^2 + (z-6)^2 = 15^2. I want to select all squares on this sphere so that its coordiantes are twelve different integer numbers like this {-8, 15, 8}, {-3, 6, 20}, {12, 9, 16}, {7, 18, 4}. I tried
ClearAll[a, b, r,…
Laurenso
- 1,032
- 2
- 11
6
votes
1 answer
Find out whether solutions exist rather than full-blown solution search
I have some quadratics, and I am trying to find out whether there exist solutions in the integers. The following tells me that the first does, wheraeas the second doesn't:
Solve[2 + 4 x + 6 x^2 == 4 - 7 y + 3 y^2 && x < 0 && y < 0, x,…
martin
- 8,678
- 4
- 23
- 70
5
votes
2 answers
How can I find four points on a circle to make a square so that its coordinates are integer numbers?
I have a circle and I want to select four points to make a square so that its coordiantes are eight different integer numbers like this
{{7, 24}, {-24, 7}, {-7, -24}, {24, -7}}
I tried
ClearAll[a, b, r, c];
a = 0;
b = 0;
r = 25;
ss = Subsets[{x, y}…
Laurenso
- 1,032
- 2
- 11
3
votes
2 answers
Diophantine equation: getting a list of solutions for each coeficient
I'm trying to solve the following diophantine equation,$$x^3+dy^3=1$$
such that $$x,y \in \mathbb{Z} \land y \neq 0$$
and I want to form a list of solutions for each $$d\in[1,1000]; d\in\mathbb{N}$$
I wrote
lista = Function[{d, i},
…
SilverShad0wz
- 197
- 7
3
votes
2 answers
Diophantine inequality that's not solved
Mathematica has trouble solving this Diophantine inequality:
(* givens *)
e = 653315732497285855855422606783
f = 1697172185816328002847853765504
g = 1650189636468405601822430434691
h = 2622176396697944576102111774652
m = 10^10
FindInstance[Abs[a f…
fgrieu
- 438
- 4
- 11
2
votes
2 answers
How can I find all integer numbers so that mydistance is an integer number?
I am tring to selec two points A, B on the sphere (x-2)^2 + (y-4)^2 + (z-6)^2 ==9^2 so that EuclideanDistance[pA,pB] is an integer and coordinates of two point A, B are integer numbers.
I know that, with distance AB= 12, I tried
ClearAll[a, b, r,…
John Paul Peter
- 1,315
- 2
- 10
2
votes
1 answer
Solving a quadratic equations over integers efficiently
I want to solve a quadratic equation over the integers but the naive method is unbearably slow (considering how easy the problem is).
I have a positive non-degenerate quadratic form $Q$ on $\mathbb Z^n$(This is why I only have finitely many…
David Jaramillo
- 135
- 5