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

2 Answers
Jul 23, 2018

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

Jul 24, 2018

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.