What are the primitive Pythagorean triples with the least, same hypotenuse or side?

L Loren May 2015 516 32 Arlington, VA Jan 2, 2020 #1 What are the primitive Pythagorean triples with the least, same hypotenuse or side?

romsek Math Team Sep 2015 2,961 1,674 USA Jan 2, 2020 #2 you mean like 3,4,5 and 5,12,13 Pythagorean Triple -- from Wolfram MathWorld Reactions: idontknow

L Loren May 2015 516 32 Arlington, VA Jan 3, 2020 #3 Say, where hypotenuses of two differing primitive Pythagorean triples are equal.

mrtwhs Feb 2010 737 162 Jan 3, 2020 #4 $\begin{align} 1105^2 &=47^2+1104^2\\ &=264^2+1073^2\\ &=576^2+943^2\\ &=744^2+817^2 \end{align}$ It took google 0.62 seconds to find these four. Reactions: Loren

$\begin{align} 1105^2 &=47^2+1104^2\\ &=264^2+1073^2\\ &=576^2+943^2\\ &=744^2+817^2 \end{align}$ It took google 0.62 seconds to find these four.

L Loren May 2015 516 32 Arlington, VA Jan 3, 2020 #5 mrtwhs, What is the smallest such hypotenuse with just two pairs of legs? Last edited: Jan 3, 2020

mrtwhs Feb 2010 737 162 Jan 3, 2020 #6 Don't know if it is the smallest but google gives $33^2+56^2 = 16^2 +63^2 = 65^2$

skipjack Forum Staff Dec 2006 21,480 2,470 Jan 3, 2020 #7 It is the smallest. The smallest pair with a leg in common is ((5, 12, 13), (12, 35, 37)). Reactions: Loren