Question

if x and y are two odd positive intigers,then show that x*2 + y*2 =4k + 2 for some integer k.

Answer 1

Answer:

Let x = 2p +1 and y = 2q + 1 (odd numbers)

where p & q are integers

substituting in  x² + y²

(2p+1)² + (2q+1)²

=> 4p² +4p +1 + 4q² +4q +1

=> 4(p² + q² + p + q) + 2

=> 4k +2 where k = (p² + q² + p + q) {integer as p&q are integers}