SOLUTION: use expressions for odd integers to confirm the conjecture that the product of two odd integers is an odd integer.

Question 706285: use expressions for odd integers to confirm the conjecture that the product of two odd integers is an odd integer.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
n is any natural or whole number.
Even Integer: 2n
Odd Integer: 2n+1
Let m be any whole number.
(2(n)+1)(2(n+m)+1)
4n(n+m)+2(n+m)+2n+1
=2(2n(n+m)+(n+m)+n)+1

Notice very carefully that the expression inside the outermost parentheses,
2n(n+m)+(n+m)+n, is a whole number, we may call N, so that
we have 2N+1. This is an odd number. Proved!
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