**Want to enhance this question?**upgrade the concern so it's on-topic for jajalger2018.orgematics Stack Exchange.

Closed 3 years ago.

You are watching: The sum of two odd numbers is

Any even number has the type $2n$. (Why? No issue what you make $n$ come be, $2n$ will, be divisible by $2$.).

Any weird number has the form $2n+1$. (Why? Play v this by plugging numbers right into $n$.).

So, include two strange numbers:

$$(2n+1)+(2n+1)=4n+2=2(2n+1)$$

Is your result *always* divisible by $2$? Why or why not?

Would you be able to reproduce the above with understanding?

Other option: modular arithmetic,

even number $pmod 2 equiv 0$ and

odd number $pmod 2 equiv 1$, then

(odd+odd) $pmod 2 equiv ?$

Basically friend can proceed from there:

((odd $pmod 2$) + (odd $pmod 2$)) $pmod 2$ $equiv ?$

Suppose there is greatest also integer NThenFor every even integer n, N ≥ n.Now suppose M = N + 2. Then, M is an also integer.

Hint : with your meaning of odd number : "All numbers that ends through 1, 3, 5, 7, or 9 are odd numbers." (consequently, even numbers room the number that finish with 0,2,4,6 or 8). Take two odd numbers, what are the feasible ends for this sum?

Using her approach, let $x$ it is in odd, and consider the various other odd number as $x+2k$. Climate the sum is $x+(x+2k)=2x+2k=2(x+k)$, i m sorry is even.

Let m and n be odd integers. Then, m and n have the right to be expressed together 2r + 1 and also 2s + 1 respectively, whereby r and s are integers. This only means that any type of odd number can be created as the amount of some also integer and one.

See more: Solved:Find A Rectangle Has A Perimeter Of 20M Express The Area

when substituting lets have actually m + n = (2r + 1) + 2s + 1 = 2r + 2s + 2.

## Not the answer you're looking for? Browse various other questions tagged proof-verification or ask your very own question.

site design / logo © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.12.40736

her privacy

By clicking “Accept every cookies”, friend agree ridge Exchange have the right to store cookies on your maker and disclose details in accordance v our Cookie Policy.