dark_magician_92 Posted January 15, 2011 Report Share Posted January 15, 2011 (edited) 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 y - x = 72? Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 y - x = 72? umm... nope Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 I was wondering why it looked so like a linear equation Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 I was wondering why it looked so like a linear equation i have this bad habit of not previewing my posts Quote Link to comment Share on other sites More sharing options...
0 wolfgang Posted January 15, 2011 Report Share Posted January 15, 2011 (edited) 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. We can rewrite the equation as: y2+432=x3 so y= 36 and x=12 Edited January 15, 2011 by wolfgang Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 (edited) 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 Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 We can rewrite the equation as: y2+432=x3 so y= 36 and x=12 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 Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 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 Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 15, 2011 Author Report Share Posted January 15, 2011 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 Great puzzle, Dark, I hope to see more from you. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 I turned it into one, sort of, and came out with the same answer as wolfgang Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2011 Report Share Posted January 15, 2011 I didn't use a program I worked it in my head. Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 16, 2011 Author Report Share Posted January 16, 2011 Great puzzle, Dark, I hope to see more from you. yeah sure....... Quote Link to comment Share on other sites More sharing options...
0 wolfgang Posted January 16, 2011 Report Share Posted January 16, 2011 OOOh...yes..I missed that...thank you Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 18, 2011 Report Share Posted January 18, 2011 yeah sure....... ? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 18, 2011 Report Share Posted January 18, 2011 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. Quote Link to comment Share on other sites More sharing options...
0 dark_magician_92 Posted January 22, 2011 Author Report Share Posted January 22, 2011 yes its fine ur correct!! Quote Link to comment Share on other sites More sharing options...
Question
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 by dark_magician_92Link to comment
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