Can you think of two odd numbers that has an odd number for its sum?

Question

Usually, odd number + odd number = even number. Is there any case wherein odd number + odd number = odd number?

Answer 1

Not possible. Odd numbers are always of the form 2n+1, and even numbers are always of the from 2n, where n is an integer.

Here's the proof:
Suppose you have two odd numbers, x and y.
Then since x and y are both odd, they can be written in the form.
x = 2n +1 and y = 2m +1, where n and m are both integers.

x+y
= (2n+1) + (2m+1)
= 2n + 2m + 2
= 2(n+m+1)
= 2k, where k= n+m+1 which is an integer.

Therefore, the sum of two odd numbers is always an even number.

Answer 2

There is no such case. Here is the proof.

1. Every odd number can be written as 2n+1 for some non-negative integer n. (In fact, that is the definition of "odd number"). For example, 31 = 2*15 + 1

2. Choose any two odd numbers. Write one of them as (2n+1), and write the other as (2m+1).

3. Add them together, and you get this:
(2n+1)+(2m+1) = 2n + 2m + 2 = 2*(n+m+1)

4. The sum you got was twice (n+m+1). But any number that is "twice" some integer, is even, by definition.

Answer 3

No. By definition an odd number is an even number + 1. So, when we add two odd numbers, we are in effect adding two even numbers and then 2. That is bound to be an even number.

If x and y are two odd numbers, each of them can be expressed as (x - 1) + 1 and (y - 1) + 1 respectively. If we add them x + y = (x - 1) + (y - 1) + 1 + 1 = (x - 1) + (y - 1) + 2

We already know that x - 1 and y - 1 are even. So, x + y = even

Answer 4

An odd number can be modeled by the equation 2n + 1, where n is any whole number. Let's add them:

2n +1 + 2n + 1 = 4n + 2

An even number can be modeled by 2n. Let's look again at what we got when we added two odd numbers:

4n + 2 = 2(2n) + 2

Two times an even number is still even. Adding two to an even number is still even. Therefore, any two odd numbers added together will always be even.

Answer 5

Never happens!
Why?
Let 2n+1 and 2m+1 be 2 odd numbers.
Then 2n+1 + 2m+1 = 2(n+m) + 2, which
is divisible by 2, and is even.

Answer 6

That's impossible.

Answer 7

not possible