perplexus.info :: Just Math : Positively Positive

Positively Positive (Posted on 2016-10-18)

Find all pairs (A, B) of positive integers such that each of the equations
x² - A*x + B = 0 and x² - B*x + A=0 has positive integer roots.

Prove that there are no others.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (2 votes)

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Puzzle Thoughts

| Comment 8 of 10 |

Harry found three pairs that work:

(A, B) = (4, 4), (5, 6) and (6, 5),

but he wasn't able to prove that no others exist.

I don't have a full explanation for this, but I believe that there must be a closure to this puzzle after more than 6 years.

To effect the foregoing, I am reopening this puzzle to all members to come up with an analytic/ computer assisted methodology proving that these three are indeed the only valid pairs in conformity with the given conditions.

Edited on January 1, 2023, 6:57 am

Posted by K Sengupta on 2023-01-01 06:49:35

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