# Questions tagged [pythagorean-triples]

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

390 questions
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### Pythagorean triples that “survive” Euler's totient function

Suppose you have three positive integers $a, b, c$ that form a Pythagorean triple: $$a^2 + b^2 = c^2. \tag{1}\label{1}$$ Additionally, suppose that when you apply Euler's ...
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2answers
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### Fermat's Last Theorem for Negative $n$

While studying Fermat's Last Theorem and Pythagorean triples, the following question occurred to me: For the equation $a^n+b^n=c^n$, where $n$ is a negative integer, a) does a solution exist, and b) ...
1answer
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2answers
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### Is there a way to find a pythagorean triple so that when you place a given digit before it, it still is a pythagorean triple?

For example, in base 10: $$5^2 + 12^2 = 13^2$$ And when I put a one before each number, the equality still holds: $$15^2 + 112^2 = 113^2$$ So my question is, in a given base, is there a way to get ...
2answers
487 views