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