Question

The sum of 2 consecutive odd integers is always a multiple of 4. Providing proof, is the statement true or false?

Answer 1

This statement is true

Explanation:

Let `m` and `n` be two consecutive odd integers:
Sums of `m` and `n`
`3+5=8`
`5+7=12`
`7+9=16`
`(-1)+(-3)=-4`

This statement is true

I used inductive reasoning, for a proof with deductive reasoning, refer to the answer above

Answer 2

True

Explanation:

Consider: `(2n-1)` for any `n in ZZ` is an odd integer.

The next consecutive odd integer will be: `(2n+1)`

Sum `= (2n-1) + (2n+1) = 4n`

Hence, the sum of any two consecutive odd integers will be a multiple of 4.