Pythagorean Triangle/Examples/693-1924-2045
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Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $693$, $1924$ and $2045$ is a primitive Pythagorean triangle.
Proof
\(\ds 693^2 + 1924^2\) | \(=\) | \(\ds 480 \, 249 + 3 \, 701 \, 776\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 4 \, 182 \, 025\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2045^2\) |
It follows by Pythagoras's Theorem that $693$, $1924$ and $2045$ form a Pythagorean triple.
Note that $693$ and $1924$ are coprime.
Hence, by definition, $693$, $1924$ and $2045$ form a primitive Pythagorean triple.
The result follows by definition of a primitive Pythagorean triangle.
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$