And you could prove that n(2m+1) is in integer by just going through the motions of proving that 2m is an integer, +1 is still an integer, etc. Anyway, it "stands to reason" that n(2m+1) is an integer, that'll do me, cuz I aint that strict!!

]]>I may have to change my answer after thinking, but here is my "gut feel":

An even number is, by definition, able to be divided evenly by 2. So any whole number multiple of an even number (the multiple could be odd or even) must also be able to be divided evenly by 2.

In algebra it may go something like this:

A number "x" is even if x=2n, where n is an integer

And a number "y" is odd if y=2m+1, where m is an integer

So, multiplying any "x" and "y" gives: xy=2n(2m+1)

But we know the definition of even is 2 times an integer ...

So, if n(2m+1) is an integer (we may need to prove that ), then

2n(2m+1) will be even, and xy must be even.

thanks so much for that!

just one more thing on that, do we just assume that **2n(2m+1)** is even, or is this because by using the 2 before the brakctes, we are saying everything is mulitplied by 2 and therefor even?

You can use powers of 10 any time, really. Scientists love them, even for small numbers like 1.2 x 10^3 instead of 1200.

]]>For example 5 = five

50 = fifty

100 = one hundred

1 000 = one thousand

100 000 = one hundred thousand

As far as I know we get to a trillion what continues on from there. I have look in many places for such a chart to describe this but have been unable to find one. Thanks for that

]]>An even number is, by definition, able to be divided evenly by 2. So any whole number multiple of an even number (the multiple could be odd or even) must also be able to be divided evenly by 2.

In algebra it may go something like this:

A number "x" is even if x=2n, where n is an integer

And a number "y" is odd if y=2m+1, where m is an integer

So, multiplying any "x" and "y" gives: xy=2n(2m+1)

But we know the definition of even is 2 times an integer ...

So, if n(2m+1) is an integer (we may need to prove that ), then **2**n(2m+1) will be even, and xy must be even.

but how could you show this is algebra?

any help is much appreciated

thanks

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