### Instruction: The difference between the squares of two different primes is 1488. Given both primes are less than 50, find the primes.

Note: Submit the numbers in either order separated by a comma.### Response: I know that the square of a number is the same as multiplying it by itself.
For example, 3 squared is 3 times 3, or 9.
So I want to find two primes that have a difference of 1488 when I square them.
One way to approach this problem is to list out the squares of the primes less than 50 and see if I can spot a pair that has a difference of 1488.
There are 15 primes less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
Squaring them, I get: 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, and 2209.
Now I want to find two of these numbers that have a difference of 1488.
I could try subtracting each number from every other number, but that would take a long time.
A faster way is to start from the largest number, 2209, and subtract 1488 from it.
This gives me 721.
Then I can check if 721 is one of the squares on my list.
It is not, so I can eliminate 2209 as a possible candidate.
Next, I move on to the second largest number, 1849, and subtract 1488 from it.
This gives me 361.
I see that 361 is on my list, so I have found a pair of squares that have a difference of 1488: 1849 and 361.
To find the primes that correspond to these squares, I need to take the square root of each number.
The square root of 1849 is 43, and the square root of 361 is 19.
These are both primes, so I have found the solution.