-2
votes
1answer
74 views

Project Euler - task №390.

When this task was not clear what the equation to be solved. This equation? $x^2y^2+z^2y^2+x^2z^2=r^2$ in integers. It is not clear, because this equation is quite simple and I do not think that ...
1
vote
1answer
46 views

Heronian isosceles triangles

This is a problem from Project Euler, problem 94. The problem asks about isosceles triangles with integer sides (differing by 1 unit, e.g, 5-5-6) and integer area, which are known to be Heronian ...
8
votes
0answers
594 views

How many integer solutions to a diophantine equation

Starting with the equation: $\frac{1}{a}+\frac{1}{b}=\frac{p}{10^n}$, I reached the equation: $10^{n-log(p)} = \frac{ab}{a+b}$. Now given the positive integer $n$, for what integer values of $p$ ...
3
votes
2answers
282 views

Solving $x^2 \cdot y^2 + x^2 + y^2 = c^2$ with $x$, $y$, $c \in \mathbb{Z}^+$

I am working on Project Euler 390. The question is about triangles, and finding the area of a triangle with sides $\sqrt{a^2+1}, \sqrt{b^2+1}$ and $\sqrt{a^2+b^2}$, with $a, b \in \mathbb{Z}$. I have ...
2
votes
3answers
567 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 ...