show-that-if-n-is-odd-n-n-2-3-is-even-

Question Number 118180 by mathocean1 last updated on 15/Oct/20

s h o w t h a t i f n i s o d d, n (n^{2} + 3) i s e v e n .

Answered by floor(10²Eta[1]) last updated on 15/Oct/20

if n is odd \Rightarrow n = 2 k + 1, k \in Z

(2 k + 1) ({(2 k + 1)}^{2} + 3)

= (2 k + 1) ({4 k}^{2} + 4 k + 4)

= 4 (2 k + 1) (k^{2} + k + 1) = even because

{it}^{'} s a multiple of 2

Commented by mathocean1 last updated on 15/Oct/20

t h a n k s