I am not sure how to write a proof that finds all cases that

I am not sure how to write a proof that finds all cases that fit the hypothesis of this claim.

(4 pts) Prove or disprove the following statement: If the product of two consecutive integers is not divisible by 3, then the sum of these two numbers is divisible by 3. 2.

Solution

Product of two consecutive numbers is not divisible by 3 means none of them is divisible by 3

Hence the numbers are of form: 3m+1,3m+2

Sum of these two numbers is:

3m+1+3m+2=6m+3 which is divisible by 3

Hence proved.