8
perfect squares
12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.
15 and 16
The difference between the squares of two consecutive integers j and j+1 is |2j+1|. There are therefore two such pairs where this quantity is 17:-9 and -88 and 9
They are: 7 and 5 because 49-25 = 24
They are perfect squares.
Every odd number greater than one is the difference of two squares. This includes all the odd prime numbers. To find the two numbers whose difference of squares equals a particular odd number, divide the odd number by 2. The two numbers are the integers immediately below and above that dividend. For example, 17 is the difference of two squares. Divide 17 by 2 and get 8.5. The two numbers are 8 and 9. 92 - 82 = 81 - 64 = 17.
Two primes whose squares have a difference of 42 are 7and 11.
The numbers are 13 and 14.
8
perfect squares
The proposition in the question is simply not true so there can be no answer!For example, if given the integer 6:there are no two perfect squares whose sum is 6,there are no two perfect squares whose difference is 6,there are no two perfect squares whose product is 6,there are no two perfect squares whose quotient is 6.
12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.
15 and 16
17 and 18
62 and 63