00:01
Hello, let's recap the question.
00:01
We have to prove the following statement by any method.
00:03
Indicating clearly which proof method is used.
00:06
We have been given, if a, b, c are odd, we have to prove that a square plus b square plus c square is odd.
00:16
And we have to recall that an integer is odd, it gets written in the form of 2k plus 1 where k is an integer.
00:22
Given a, b, c are all integers, we can express them in the form of 2k plus 1 where k is an integer.
00:27
So we have a is equal to 2k1 plus 1, b is equal to 2k2 plus 1 and c is equal to 2k2 plus, sorry 2k3 plus 1 where k1, k2 and k3 are integers.
00:44
Let's compute a square of the property square which will be 2k1 plus 1 whole square plus 2k2 plus 1 whole square plus 2k3 plus 1 whole square which comes out to be 4k1 square plus 4k1 plus 1 plus 4k2 whole square plus 4k2 plus 1 plus 4k3 whole square plus 4k3 plus 1...