# Primitive Pythagorean triples with the least, same hypotenuse or side

#### Loren

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

#### Loren

Say, where hypotenuses of two differing primitive Pythagorean triples are equal.

#### mrtwhs

\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.

Loren

#### Loren

mrtwhs,

What is the smallest such hypotenuse with just two pairs of legs?

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#### mrtwhs

Don't know if it is the smallest but google gives $33^2+56^2 = 16^2 +63^2 = 65^2$

#### skipjack

Forum Staff
It is the smallest. The smallest pair with a leg in common is ((5, 12, 13), (12, 35, 37)).

Loren