Question

The sum of any two different odd numbers is divisible by 4.

Answer 1

Explanation:

are 1 and 3, then their sum is 4 which is divisible by 4.

are 3 and 5, their sum is 8 which is divisible by 4.

Answer 2

False

Explanation:

counterexample: 3 + 7 = 10 . . . . not divisible by 4

The statement is FALSE.

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An odd number can be represented by ...

2n+1 . . . . where n is any integer

Then a different odd number can be represented by ...

2m +1 . . . . where m is any integer

The sum of these numbers will be ...

(2n +1) +(2m +1) = 2n +2m +2 = 2(n +m +1)

This will be divisible by 2 for any integers m and n, but will only be divisible by 4 if exactly one of the integers m and n is odd.