3
votes
2answers
79 views

Generating Pythagorean Triples S.T. $b = a+1$

I am looking for a method to generate Pythagorean Triples $(a,b,c)$. There are many methods listed on Wikipedia but I have a unique constraint that I can't seem to integrate into any of the listed ...
5
votes
3answers
423 views

Prime Number in triangle

I had a question here, the measures of the sides of a right triangle (a single unit) can be prime numbers? If they can not, why?! But, if you can, could you help me find an example?
4
votes
4answers
326 views

Is every prime number the leg of exactly one right triangle with integer sides? What's wrong with my argument that this is impossible?

The problem is: "prove that every prime number is the leg of exactly one right triangle with integer sides." However, I seem to have proved that this is impossible. What did I do wrong here? Let ...
1
vote
1answer
174 views

Irrational distances, rational area triangles

Given any positive integer $n\ge3$ how to show that there are $n$ distinct points in the plane such that 1- the distance between any two points is irrational number and 2- each set of three points ...
3
votes
1answer
235 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 ...
10
votes
3answers
163 views

For which n are there primitive Pythagorean triples with legs of lengths a and a+n?

For which n can $a^{2}+(a+n)^{2}=c^{2}$ be solved, where $a,b,c,n$ are positive integers? I have found solutions for $n=1,7,17,23,31,41,47,79,89$ and for multiples of $7,17,23$... Are there ...