Tagged Questions
3
votes
4answers
137 views
Integral solutions of hyperboloid $x^2+y^2-z^2=1$
Are there integral solutions to the equation $x^2+y^2-z^2=1$?
1
vote
0answers
66 views
Finding integer coordinates on a sphere's surface [duplicate]
Possible Duplicate:
Integer coordinate set of points that is a member of sphere surface
Assume $C$ is a sphere with radius $r$ and center in the origin (0,0,0). How can we find the set of ...
2
votes
2answers
169 views
rational triangles and cosines
I've recently started to try working on exercises from this book on Diophantine equations before I need to return it to the library. This one has me slightly stumped. It asks to show that the cosine ...
2
votes
1answer
194 views
Heronian triangles
How to prove that all Heronian triangles can be found using formulas described here?
I understand that the described substitution will give Heronian triangle, but how to prove that using the ...
3
votes
2answers
251 views
Heronian triangle Generator
I'm trouble shooting my code I wrote to generate all Heronian Triangles (triangle with integer sides and integer area). I'm using the following algorithm
$$a=n(m^{2}+k^{2})$$
$$b=m(n^{2}+k^{2})$$
...
3
votes
1answer
458 views
Integer coordinate set of points that is a member of sphere surface
I have a graphic application to develop which involve many spheres. I should determine then on run time.
Supposing that I have a sphere of radius r, how can I determine the sub set of the sphere ...
8
votes
5answers
397 views
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
I'm fairly certain it does, but I'm hoping to see a rigorous proof of this statement. Thanks.
Here is my motivation. I'm ...
2
votes
3answers
423 views
Primitive integer triangles
Consider the triangles with integer sides a, b and c with a ≤ b ≤ c.
An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1.
How many primitive integer sided triangles exist with a ...
