|Bill Allombert on Tue, 02 Aug 2022 10:46:28 +0200|
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|Re: solving x^3-ay^3=1 over integers (N)|
On Tue, Aug 02, 2022 at 08:26:03AM +0200, Ralph Beckmann wrote: > Good morning, > > I am new to PARI and I would like to use it on cubic Pell equations. > > Can anyone show me how to solve x³-ay³=1 (a,x,y ∈ ℕ)? Hello Ralf, There are several ways to handle such equations, but the simplest with PARI/GP is to consider this as a Thue equation with P(x,y)=x³-ay³ In PARI/GP this is done as follows thue(x^3-a,1) For example for a=37 ? thue(x^3-37,1) %42 = [[1,0],[10,3]] which meant that the solution are (x,y)=(1,0) and (x,y)=(10,3) and indeed 10^3-37*3^3=1 Cheers, Bill.