#### lentesta

##### Well-Known Member

Hence, adding two odd numbers always results in an even number.

- Definition of odd and even numbers: An integer n is defined as even if it can be written in the form n = 2k, where k is also an integer. An integer n is defined as odd if it can be written in the form n = 2k + 1, where k is an integer.
- Proof: Let m and n be two odd numbers, so m = 2k + 1 and n = 2l + 1, where k and l are integers.
- Adding the two odd numbers: m + n = (2k + 1) + (2l + 1) = 2k + 2l + 2 = 2(k + l + 1), where k + l + 1 is also an integer.
- Conclusion: Since m + n can be written in the form 2(k + l + 1), it is an even integer.

Elevating discourse on this forum since 2016, folks. Thanks @MisterPenguin.