Question

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

Answer 1

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

Answer 2

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

Answer 3

That's it?

Answer 4

(that's my solution btw)

Answer 5

seems good enough to me..

Answer 6

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

Answer 7

Thanks, another one coming up...

Answer 8

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

Answer 9

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

Answer 10

mocking again eh? :|
bah,nevermind..