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Positively Positive (Posted on 2016-10-18) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Part 1 only (spoiler) Comment 7 of 7 |

I can find three pairs that work:

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

but I can't yet prove that no others exist.

They must lie in the 1st quadrant of the A-B plane 'outside' the parabolas a^2 = 4b and b^2 = 4a and there's plenty of room to explore there...

  Posted by Harry on 2016-10-19 17:15:01
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