- #1

- 48

- 0

I'm trying to find the integer solutions for

6n^2 -18n +16 = m^2

using pell equation, any idea

please help

thanks

- Thread starter 76Ahmad
- Start date

- #1

- 48

- 0

I'm trying to find the integer solutions for

6n^2 -18n +16 = m^2

using pell equation, any idea

please help

thanks

- #2

disregardthat

Science Advisor

- 1,854

- 33

Try to write 6n^2-18n in a different way to make the equation look like a standard pell equation.

- #3

- 48

- 0

I tryed and found this form:

3/2 (2n-3)^2 -m^2 = -5/2

3/2 (2n-3)^2 -m^2 = -5/2

- #4

- 48

- 0

OR

m^2 - 3/2 (2n-3)^2 = 5/2

m^2 - 3/2 (2n-3)^2 = 5/2

- #5

- 48

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and by multiply the second form with 2/5 I get

2/5 m^2 - 3/5 (2n-3)^2 = 1

2/5 m^2 - 3/5 (2n-3)^2 = 1

- #6

- #7

- 95

- 2

- #8

- 95

- 2

Some solutions with negative n: (-5,16), (-14, 38), (-63,158), (-152,376), (-637,1564)

- #9

- 48

- 0

but how I know all the +solutions as large as I can.

what steps you follow so you found these solutions?

(no negativs solutions)

- #10

- 95

- 2

It goes like this:

For n = 0 to 999 do

[itex]\space\space\space[/itex]w= 6*n[itex]^{2}[/itex]-18*n+16

[itex]\space\space\space[/itex]If w is a perfect square i.e. w=m[itex]^{2}[/itex]

[itex]\space\space\space\space[/itex] then Return (n,m)

[itex]\space\space\space[/itex]end_If

end_For

...sort of experimental math !

- #11

- 84

- 0

but how I know all the +solutions as large as I can.

what steps you follow so you found these solutions?

(no negativs solutions)

You go on Alperton's site ( which I provided above in my first post ) and you enter your parameter to that your equation becomes:

6 x2 - y2 - 18 x + 16 = 0

and you click on solve it and it does it for you. Now under Modes ( below the solve it button ), you have two choices:

1- just solution ( for when you are in a hurry )

2- step by step ( for when you want to in fact learn something )

if you choose step by step, you will be taught how to solve this kind of equation. But if you do not take the time to check every single post ( like mine above ), then you may miss some important stuff.

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