### 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: A possible strategy is to start with the largest prime less than 50, which is 47, and see if 47^2 - p^2 = 1488 for some prime p.
Expanding the left side, we get 2209 - p^2 = 1488, or p^2 = 721.
721 is not a perfect square, so 47 cannot be one of the primes.
The next largest prime is 43, so we try 43^2 - p^2 = 1488.
This gives us 1849 - p^2 = 1488, or p^2 = 361.
361 is a perfect square, namely 19^2, and 19 is also a prime.
So we have found the two primes: 43 and 19.