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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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Some Thoughts Another way. | Comment 5 of 7 |

Using the Polynomial roots formula,

x^2 coefficient  = 1 
Roots (p+q) = A 
Roots (pq) = B 
 
x^2 coefficient  = 1 
Roots (r+s) = B 
Roots (rs) = A

it is easy to derive p=q and r=s; then 2p=r^2, 2r=p^2, p=q=r=s=2, {A,B} ={4,4} as the sole solution in the positive integers.

(Other solutions not compliant with the terms of the puzzle are also possible.)


  Posted by broll on 2016-10-19 06:19:44
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