# Questions tagged [pythagorean-triples]

Questions about Pythagorean triples, positive integer solutions to $a^2 + b^2 = c^2$.

59 questions
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### The Jacobi-Madden equation $a^4+b^4+c^4+d^4 = (a+b+c+d)^4$ and disguised Pythagorean triples

I. The Jacobi-Madden equation, $$a^4+b^4+c^4+d^4 = (a+b+c+d)^4$$ is equivalent to a disguised Pythagorean triple, $$(a^2+ab+b^2)^2+(c^2+cd+d^2)^2 = \big((a+b)^2+(a+b)(c+d)+(c+d)^2\big)^2$$ II. A ...
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### Generating Pythagorean Triples from Others via Dissections

Roger Alperin's paper Modular Tree of Pythagoras shows it is possible to generate Pythagorean triples from others. If $a,b,c$ are the sides of a right triangle $a^2 + b^2 = c^2$ then we can derive ...
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### Need help with proof about Diophantine equations

The way I am planning to arrange this is by providing fragments of the proof, so I can understand what's going on before forging ahead, so if you are going to help me, keep in mind that I am going to ...
This is a followup question to: Product of slopes of rational points on the unit circle (related to pythagorean triples) mathlove correctly showed that $D=1$ gives an infinity of solution pairs. But ...