Question

Prove that there exist three consecutive positive integers that the square of the largest integer is the sum of the squares of two smaller integers. We find that 52 = 42 + 32. It is approved. What is this proof method called?

Answer 1

The proof method used in this question is called direct proof or proof by example. To prove the statement, we can provide a specific example of three consecutive positive integers where the square of the largest integer is the sum of the squares of two smaller integers.

Step-by-step explanation:

The proof method used in this question is called direct proof or proof by example.

To prove that there exist three consecutive positive integers where the square of the largest integer is the sum of the squares of two smaller integers, we can simply provide an example. In this case, we have 5, 4, and 3 as the three consecutive positive integers. The square of 5 is 25, and the sum of the squares of 4 and 3 is also 25.

Therefore, the statement is proven because we have provided a specific example that satisfies the condition.