[dark_magician_92]

Find all integer solutions of y2 = x3 − 432.

Try to solve this without using a computer program

All the best!!

and i agree this is a dumb title i have come up with.

Edited January 15, 2011 by dark_magician_92

[Guest]

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y - x = 72?

[dark_magician_92]

  On 1/15/2011 at 1:58 PM, Darth Legion said:

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y - x = 72?

umm... nope

[dark_magician_92]

hey everyone i m really sorry for my carelessness, its y^2=x^3-432, not y2,x3 and all that, i regret for being careless, this wont be repeated in future.

[Guest]

I was wondering why it looked so like a linear equation

[dark_magician_92]

  On 1/15/2011 at 3:13 PM, Darth Legion said:

I was wondering why it looked so like a linear equation

i have this bad habit of not previewing my posts

[wolfgang]

  On 1/15/2011 at 10:49 AM, dark_magician_92 said:

Find all integer solutions of y2 = x3 − 432.

Try to solve this without using a computer program

All the best!!

and i agree this is a dumb title i have come up with.

  Reveal hidden contents

We can rewrite the equation as: y2+432=x3

so y= 36

and x=12

Edited January 15, 2011 by wolfgang

[Guest]

Seeing as it's only a linear equation and I've already played a little with it in my head I'll let someone else solve it

[Guest]

By solve I mean, post the answer. I know that won't gain me any reputation, but this is so easy for me I don't want to spoil it for anyone else. That's what I get for being a programmer lol.

Edited January 15, 2011 by Darth Legion

[dark_magician_92]

  On 1/15/2011 at 5:49 PM, wolfgang said:

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We can rewrite the equation as: y2+432=x3

so y= 36

and x=12

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very well done sir (if u did it not using a program), and yes since we r dealing with y^2, hence x-12, y=12, -12

[dark_magician_92]

  On 1/15/2011 at 7:43 PM, Darth Legion said:

By solve I mean, post the answer. I know that won't gain me any reputation, but this is so easy for me I don't want to spoil it for anyone else. That's what I get for being a programmer lol.

your wish no problem, but i was looking for an answer without using a computer program

[dark_magician_92]

  On 1/15/2011 at 5:50 PM, Darth Legion said:

Seeing as it's only a linear equation and I've already played a little with it in my head I'll let someone else solve it

it's not a linear equation

[Guest]

Great puzzle, Dark, I hope to see more from you.

[Guest]

I turned it into one, sort of, and came out with the same answer as wolfgang

[Guest]

I didn't use a program I worked it in my head.

[dark_magician_92]

  On 1/15/2011 at 9:53 PM, Darth Legion said:

Great puzzle, Dark, I hope to see more from you.

yeah sure.......

[wolfgang]

OOOh...yes..I missed that...thank you

[Guest]

  On 1/16/2011 at 6:45 AM, dark_magician_92 said:

yeah sure.......

?

[Guest]

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We remember from 7th grade algebra that a^2 –b^2 = (a+b) (a-b) and

a^3 –b^3 = (a^2+b^2+ab) (a-b)

Looking at the equation, we seek a number n to subtract from both sides whereby

Y^2 – n = x^3 – (432 + n) makes the left side a difference of squares, and the right side a difference of cubes.

By experimentation, starting with the first cube greater than 432 (8^3 = 512), we observe the following:

8^3 = 512; 512-432 = 80. 80 is not a perfect square, so we try 9 and so forth…

12^3 = 1728. 1728 – 432 = 1296, which is 36^2. So we have

y^2 - 36^2 = (x^3 - 12^3)

and

(y + 36) (y – 36) = (x^2 +12 x + 144) (x-12)

Obvious integers which make this work are at the zeroes: y = +-36 and x = 12. I don’t think there are others, but I haven’t proved it yet.

[dark_magician_92]

yes its fine ur correct!!