Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive even numbers is 1 less than a perfect square

The correct answer is: even numbers.

Let the even number be 2n. Its consecutive even number will be 2n+2
Finding the product of 2n and (2n+2)

2n(2n+2) = 2n(2n) + 2n(2)

2n(2n+2) = 4n² + 4n
The given conjecture is “The product of any two consecutive even numbers is 1 less than a perfect square”

So, add 1 to 4n² + 4n

4n² + 4n +1 = (2n)² + 2(2n)(1) + 1²

= (2n + 1)²
So, we can see that the perfect square of 2n+1 is 4n² + 4n +1 and 1 less than 4n² + 4n +1 is a product of any two consecutive even numbers.
Final Answer:
Hence, the given conjecture is right and we have proved it by Deductive reasoning.