Question

Prove product of 2 odd integers is odd

Answer 1

product is multiplication

Answer 2

is using the fact that an even number times odd number is even is fine for the proof ?

Answer 3

Let x and y be particular but arbitrarily chosen odd numbers.
Then, x = 2k+1 and y = 2l + 1, for some integers k and l.

We have x · y = (2k + 1) · (2l + 1) =
4kl + 2(k + l) + 1 = 2(2kl + k + l) + 1

Let p = 2kl + k + l. Since k and l are integers, p is an integer and x · y = 2p + 1 is odd.

Answer 4

if so :

let w,v be odd integers
so using integers p,t we might write: w = 2p + 1 , v = 2t + 1
so
w * v = (2p+1)(2t+1) = 4pt + 2p + 2t + 1 = 2(2pt+p+t) + 1
now if we let again x = 2pt + p +t is an integer
we get that w*v is odd :)