# Questions tagged [pythagorean-triples]

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

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### Pythagorean triples-number theory [closed]

How can I prove that the hypotenuse $h$ of a primitive Pythagorean triangle (that is a right triangle which sides are given by a primitive Pythagorean triple) can be written as $h=12k+1$ or $h=12k+5$...
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### Does it follow from the Pythagorean theorem that “there is no right-angled triangle with sides 5, 10 and 11”?

Assume, for the sake of this question, that we define the Pythagoeran theorem as Theorem 1: In a right-angled triangle, the sum of the squares of the two shortest sides is equal to the square of the ...
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### Pythagorian triples condition

Pythagorian triple is every triple of natural numbers $(x, y, z)$ such that $x, y, z$ are sides of right triangle, where $z$ is hypotenuse. Now, Pythagorian theorem says $x^2 + y^2 = z^2.$ (1) If we ...
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### Is there another formula which generates Pythagoras' triples such that the largest $2$ of the triple differ by $3$?

I was thinking about Pythagoras' triples recently, and I wondered if I could find a formula that generated Pythagorean triples such that the largest of $2$ numbers of the triple differ by $1$, and I ...
### Reference request: there are only two integer solutions to $2^{2a} + 3^{2b} = 5^c$. [duplicate]
I believe there are only two non-negative integer solutions to $$2^{2a} + 3^{2b} = 5^c.$$ The solutions I have are $a=1,b=0,c=1$ and $a=2,b=1,c=2$. I'm not certain this is correct. I'd like to know if ...