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Questions tagged [pythagorean-triples]

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Subtours in the Set of Pythagorean Triples

Question: Are there any examples, results about, algorithms for finding subtours in the set of pythagorean triples? By those subtours in the set of pythagorean triples I understand finite ...
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Is 100 the only Leyland number that is a square?

Leyland numbers (named for Paul Leyland) are positive integers of the form $x^y + y^x$ , where x and y are naturals > 1, and also the number 3. The OEIS link is https://oeis.org/A076980 I thought ...
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1answer
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Integer points avoiding three on a line, four on a circle

A century ago, Dudeney asked to place $16$ pawns on a chessboard with no three on a line:           As described by David Eppstein,1 the maximum number $g_3(n)$ points that ...
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Can we surround a non-rectangular area with Lego fences?

My children have some Duplo fences, these you have to put down on two points, and at both ends they extend a little where you can connect several to surround some area. So a fence is described by a ...
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Is there any formula to find number of Pythagorean triplets between two integers 2 and j, j>2?

Given $j \geq 5$, is there a formula for the number of Pythagorean triplets $(a, b, c)$ satisfying the constraint that $a, b, c \leq j$? There exists at least one Pythagorean triplet for $j\geq5$; ...
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1answer
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Realization of numbers as a sum of three squares via right-angled tetrahedra

De Gua's theorem is a $3$-dimensional analog of the Pythagorean theorem: The square of the area of the diagonal face of a right-angled tetrahedron is the sum of the squares of the areas of the other ...
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Primitive triples in a region [duplicate]

Are there at least $cn$ Pythagorean triples and at least $dn$ Primitive Pythagorean triples $(A,B,C)$ with $$2^{\frac n2}<A<2^{\frac n2+1}<2^n<B<C<2^{n+1}$$ with some fixed $0<d&...
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Sharply Estimating Pythagorean Triples [closed]

Given $m,n\in\Bbb N$ with $m<n$, how many pythagorean triples $p^2+r^2=q^2$ satisfy $$m\leq p<r\leq n?$$ Is there a way to give a sharp estimate?
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Assistance with understanding parent/child relationships in Pythagorean Triples

I want to start by apologising for what is probably a weak attempt at a question on a site like this, but I'm having trouble understand a concept that doesn't seem to be properly explained elsewhere - ...