Definition:

- A number which can be written in the form of 2 m where m is an integer, is called an even integer.
- A number which can be written in the form of 2 m + 1 where m is an integer, is called an odd integer.

2n and 2n + 1

Now add them

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

The sum is of the form 2n + 1 (2n is an integer because the product of two integers is an integer)

Therefore, the sum of two consecutive integers is an odd number.