# Questions tagged [pythagorean-triples]

The tag has no usage guidance.

17 questions
Filter by
Sorted by
Tagged with
168 views

### Reference request on a pattern among nearly isosceles Pythagorean triples

Let us understand the term nearly isosceles Pythagorean triple to mean one whose legs differ by $1.$ A fortiori such a triple is primitive. After someone asked me how to find such triples, it was easy ...
• 10.1k
1k views

### Size of set of integers with all sums of two distinct elements giving squares

Are there arbitrarily large sets $\mathcal S=\{a_1,\ldots,a_n\}$ of strictly positive integers such that all sums $a_i+a_j$ of two distinct elements in $\mathcal S$ are squares? Considering subsets in ...
• 14.3k
255 views

### Finding Pythagorean quadruples on a given plane?

In 2D one cannot construct Pythagorean triples $x^2+y^2=m^2$ ($x,y,m\in\mathbb{Z}$) that lie on every line through the origin (e.g., a Pythagorean triple with $x=y$ would require $\sqrt{2}$ to be ...
1 vote
74 views

• 1,748
282 views

### Triangulating the plane using edges of unique rational lengths

Basic question: Can the Euclidean plane be divided into a vertex-to-vertex arrangement of non-overlapping triangles such that every edge has a unique rational length that lies between 1 and some ...
• 3,551
868 views

### Prove $\frac{\text{Area}_1}{c_1^2}+\frac{\text{Area}_2}{c_2^2}\neq \frac{\text{Area}_3}{c_3^2}$ for all primitive Pythagorean triples

A while ago I asked this question on MSE here. After placing a bounty it got quite a bit of attention but unfortunately it has yet to be resolved. After getting some advice from MO Meta I have decided ...
• 211