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

Respuesta :

unicorn3125

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

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