perplexus.info :: Just Math : Cubic and Quadratic Determination

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

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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