Show that $ka,kb,kc$ where $k \in \mathbb{N}$ is a Pythagorean Triplet if $a,b,c$ is a Pythagorean Triplet.

Question

parthkohli · Answer

Only use $(ka)^2 + (kb)^2 = (kc)^2$? Simplifies to:$$k^2a^2 + k^2 b^2 = k^2c^2$$Divide both sides by $k^2$.$$a^2 + b^2 = c^2$$

parthkohli · Answer

Note that the second step is due to the theorem/lemma that if $n \in \mathbb{N}$, then $n^2 \in \mathbb{N}$.

parthkohli · Answer

That's it?

parthkohli · Answer

(that's my solution btw)

shubhamsrg · Answer

seems good enough to me..

parthkohli · Answer

Seems that Christmas has brought me the enlightenment of proofs =/

parthkohli · Answer

Thanks, another one coming up...

shubhamsrg · Answer

my side of the story is that things strike like an epiphany to me irrespective of the festive season!

parthkohli · Answer

@shubhamsrg That seems legit seeing the quality of your solutions :)

shubhamsrg · Answer

mocking again eh? :|
bah,nevermind..