# math Q: about Pythagorean Triples **URL:** \ **Category:** Factual Questions\ **Created:** [March 1, 2008, 10:34pm UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780 "2008-03-01T22:34:56Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [March 1, 2008, 10:34pm UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/1 "2008-03-01T22:34:56Z")
Pythagorean Triples are whole numbers that fit the famous formula of A[sup]2[/sup] + B[sup]2[/sup] = C[sup]2[/sup]. The lowest example being 3, 4, and 5. I was interested in triples where A and B differ by only 1. Other examples are 20,21, 29; 119, 120, 169; and 696, 697, 985. I found those examples through a formula\* that does always yield triples where A and B differ by one; however, I don’t know if the formula gives all instances, or if there might be others that I’m missing. Any math wizs care to take a crack at this? \*the details would be three times longer than this post, but I’ll post it if anyone wants. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 1, 2008, 10:48pm UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/2 "2008-03-01T22:48:49Z")
Are you asking to verify a fact about a formula that we don’t know? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [March 1, 2008, 10:50pm UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/3 "2008-03-01T22:50:19Z")
Hehe. I’m guessing his formula is [this one](http://en.wikipedia.org/wiki/Pell_number#Pythagorean_triples). ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [March 1, 2008, 11:07pm UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/4 "2008-03-01T23:07:16Z")
Mathworld has more information than you ever wanted on [Pythagorean Triples](http://mathworld.wolfram.com/PythagoreanTriple.html). What you’re asking about are [Twin Pythagorean Triples](http://mathworld.wolfram.com/TwinPythagoreanTriple.html), specifically, what mathworld calls “leg-leg” twin Pythagorean triples. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [March 2, 2008, 12:40am UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/5 "2008-03-02T00:40:04Z")
I’ll have to read it in more detail later, but it looks like Pell numbers as applied to leg-leg Pythagorean triples is exactly what I was looking for. Thanks! ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [March 2, 2008, 2:15am UTC](https://boards.straightdope.com/t/math-q-about-pythagorean-triples/439780/6 "2008-03-02T02:15:28Z")
Ah! In general, I was using what I didn’t know were the Pell sequence numbers (0, 1, 2, 5, 12, 29, 70, etc.) to generate leg-leg Pythagorean triples. I knew that the terms of that series approximated √2 +1, but I didn’t have a justification for using only those numbers, or proof that all leg-leg triples would have to fit that sequence. Case closed.