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        riddles >> medium >> Pell equations
        
(Message started by: Christine on Sep 29th, 2015, 11:10pm)
Title: Pell equations
Post by Christine on Sep 29th, 2015, 11:10pm
can you find solutions to

x^2 + k*y^2 = a^2
x^2 -  k*y^2 = b^2

for k = 13,31,37,46,47,53,61,71,79

with GCD (x,y) = 1
Title: Re: Pell equations
Post by pex on Sep 30th, 2015, 4:38pm
For k=46, x=7585 and y=924 works.
Title: Re: Pell equations
Post by towr on Oct 1st, 2015, 10:59pm
x=1, y=0 works :P
Title: Re: Pell equations
Post by pex on Oct 5th, 2015, 7:11pm
For k=13, there's x=106921 and y=19380. (Yes, I'm just running a simple brute force search.)
Title: Re: Pell equations
Post by pex on Oct 16th, 2015, 11:38pm
Current status:

1069212 + 13*193802 = 1277292
1069212 - 13*193802 = 809292

25665612 + 31*2066402 = 28126392
25665612 - 31*2066402 = 22942392

75852 + 46*9242 = 98392
75852 - 46*9242 = 42732

129746412 + 71*5636402 = 138165592
129746412 - 71*5636402 = 120741592


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