Tagged Questions

4answers
137 views

Integral solutions of hyperboloid $x^2+y^2-z^2=1$

Are there integral solutions to the equation $x^2+y^2-z^2=1$?
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 ...
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 ...
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 ...
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 $$a=n(m^{2}+k^{2})$$ $$b=m(n^{2}+k^{2})$$ ...
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 ...
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 ...
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 ...
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