Question

odd integer * odd integer = ?
explain please :)

Answer 1

That will also be an odd integer:

Let "x" be an odd integer: that means there is some integer "n" (odd or even) such that:

x = 2n + 1

Similarly, for another odd integer, "y":

y = 2m + 1

The product is:

xy = (2n + 1)(2m + 1) = 4mn + 2m + 2n + 1
= 2(2mn + m + n) + 1

So, we have another expression that has 2 terms. The first is multiplied by 2, giving us an even number, but we add 1 to it, making xy odd.

Answer 2

"2mn + m + n" the expression is parentheses, is just another integer, acting the same as "m" or "n" in the definition of "x" and "y".

Answer 3

All good now, @ontour ?

Answer 4

Yes thank you! :)

Answer 5

uw! Good luck to you in all of your studies and thanks for the recognition! @ontour

Answer 6

no problem@