Question

Use expressions for odd integers to confirm the conjecture that the product for two odd integers is an odd integer.

Answer 1

k, n - integers

2k+1 - an odd integer

2n+1 - another odd integer

The product of them:

(2k + 1)(2n + 1) =

= 4kn + 2k + 2n + 1 =

= 2(2kn + k + n) + 1

The product of integers (2kn) is integer

and the sum of them (2kn+k+n) also is integer

So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer