Simple algebra: odd x odd = even?

Question

Is it possible? If so, what are the numbers?

Answer 1

No.

But I can't think of a mathematical way of demonstrating it.

Basically, if you look at it like this....an odd number, when divided by two, leaves 1 leftover. So if you were to multiply by another odd number, all those leftover ones are still going to add up to another odd number.

d**n.

That made little sense.

I hope SOMEONE has a proper, mathematical proof for this. I want to know what it is.

Answer 2

odd x odd = odd

1x1=1

3x3=9

5x5=25

7x7=49

9x9=81

11x11=121

13x13= 169

etc

Answer 3

odd x odd = odd always

Answer 4

No, it is not possible, and here's why.

Assume that any odd number is 2n+1, where n is an integer. If we multiply this with another odd number, which is also 2n+1, we get this:

(2n+1)(2n+1)

= 4n² + 4n + 1

Because the coefficient of the n terms is even, we know that they will result in even numbers, so long as n is an integer. But because we have the +1 on the end, this will ensure that the result changes to an odd number, hence an odd number multiplied by an odd number will always produce an odd result.

Answer 5

2n is by definition an even number (a number divisible by 2)

2n + 1 is an odd number

Take 2 odd numbers (2m + 1) and (2n + 1)

The product of these odd numbers is:

(2m + 1)(2n + 1) = 4mn + 2m + 2n +1 = 2(2mn +m + n) + 1 = 2p + 1, another odd number.

So "odd x odd = even" is impossible

Answer 6

Odd x odd always results in an odd product.