How to create these sorts of proofs, begin by finding the following. (1) a perfect number is a positive integer that is equal to the sum of all of its proper integer divisors. (for example, the integer 4 is not perfect, because its proper divisors are 1 and 2. 1+2 4.) find a perfect number and justify your answer. (2) find a pair of consecutive integers such that one of the integers is a perfect square, and the examples and justifications above are exactly what you would use to make is called a constructive existence proof of the following theorems: theorem 1. there enists at least one perfect number what theorem 2. there erists a pair of consecutive integers such that one integer is a perfect square, and the other is a perfect cube. note that not all existence proofs are constructive though!