Discrete Maths Help

Question

For the following ‘proof’, find the mistake and explain how it can be rectified.

Theorem: There exists a natural number that is divisible by 6, and that can be written as (n + 1)(n + 2), for some natural number n.

Proof: Let us consider the number 18; 18 is of the form (n + 1)(n + 2) and 18 is divisible by 6. Hence we have found a number witnessing that the theorem is true.

Answer 1

The number 18 is not of the form (n+1)(n+2). Change 18 to 12=(3 times 4) and the proof is correct.