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 Cubic and Quadratic Determination (Posted on 2016-05-14)
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 No Rating

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 re(2): Possible solution Comment 3 of 3 |
(In reply to re: Possible solution by Jer)

this is an elliptic curve and a known property of elliptic curves is that the set of integer points is finite.  Using the following two lines in Maga

E:=EllipticCurve([0,0,0,1,-1]);
IntegralPoints(E);

you can see that these 3 points are the only ones with positive cooridnates.  This can be ran for free at the following link

http://magma.maths.usyd.edu.au/calc/

 Posted by Daniel on 2016-05-16 09:13:02

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