Sum of two consecutive numbers is always odd

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Sum of two consecutive numbers is always odd

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.

Take two consecutive integers, one even, and one odd:
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.