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Topic: Pell equations (Read 650 times)

Christine
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Pell equations
« on: Sep 29^th, 2015, 11:10pm »

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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

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pex
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Re: Pell equations
« Reply #1 on: Sep 30^th, 2015, 4:38pm »

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For k=46, x=7585 and y=924 works.

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towr
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Re: Pell equations
« Reply #2 on: Oct 1^st, 2015, 10:59pm »

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x=1, y=0 works Tongue

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pex
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Re: Pell equations
« Reply #3 on: Oct 5^th, 2015, 7:11pm »

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For k=13, there's x=106921 and y=19380. (Yes, I'm just running a simple brute force search.)

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pex
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Re: Pell equations
« Reply #4 on: Oct 16^th, 2015, 11:38pm »

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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

« Last Edit: Dec 21^st, 2015, 7:02am by pex »

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