Find all possible pairs (x, y) of prime numbers, with x less than or equal to y, and each of x and y being less than 2023, such that:
• y divides x2 + 8 and,
• x divides y2 + 8
Provide valid reasoning as to why there are no further solutions.
*** Extra credit for an analytical solution.
Note: This puzzle is adapted from a problem appearing in the Zhautykov Olympiad.
(In reply to
Computer solution without extra credit by Larry)
(89,881)
This is why I was having such a hard time proving there were no "large" solutions - because that premise is false! I found (2,2) and (3,17) pretty quickly and thought that since this was an Olympiad problem the rest of the answer would be to prove the lack of "large" solutions. Now I see that is not the case and am at a loss to figure how to get to (89,881).
re: Computer solution without extra credit
