perplexus.info :: Numbers : Prime Crossed Factor Puzzle

Prime Crossed Factor Puzzle (Posted on 2023-03-18)

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.

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

{x,y} = {2,2}, {3,17}, {89, 881}.
For an explanation, refer to the solution submitted by broll in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Possible Solution	broll	2023-03-19 03:38:45
re: Computer solution without extra credit	Brian Smith	2023-03-18 21:05:44
Computer solution without extra credit	Larry	2023-03-18 08:23:01

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