This the question:
Q: Prove or disprove the following statement.
The difference of the square of any two consecutive integers is odd
This is working step:
let $m,m+1$ be 2 consective integers:
$$(m+1)^2-m^2$$
$$m^2+1+2m-m^2$$
$$1+2m$$
If $m$ is odd then $2m=\text{even}$,
if $m$ is even then $2m=\text{even}$,
then adding $1$ will make it odd.
Can you please advise me if my working is the right step and could I answer like this? I am new to discrete and not sure if I can ans like this. Feedback is welcome to improve the presentation of the steps 🙂
Best Answer
The fact that ...$2m$ is always even , then $2m+1$ is odd regardless of ...$m$.