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Cubic and Quadratic Determination (Posted on 2016-05-14) Difficulty: 3 of 5
Each of P and Q is a positive integer such that:
P3+P-1= Q2

Find the three smallest values of P+Q

No Solution Yet Submitted by K Sengupta    
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re: Possible solution | Comment 2 of 3 |
(In reply to Possible solution by armando)

I was surprised by two things:
1. How easy it was to find three solutions.  I expected at least one of them to be big enough to be hard to find. 

2. How hard it is to find four solutions.

In searching up to P=10000 there is no other solution.  There is a near solution at p=3532 which my little calculator program flagged.  I can't search further this way because I'm up against my digital precision.

I tried narrowing things down by going mod 2,3,5,7,11 and although this puts some constraints on P (and Q) it doesn't seem to point the way.

  Posted by Jer on 2016-05-14 14:45:28

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