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 September 18th, 2018, 01:54 PM #1 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 how to show that 2n + 1 = x ^ 2 ? how to show that 2n + 1 = x ^ 2 ? the solution is: n = 2 * (m ^ 2 - m) x = 1 - 2 * m and 1 + 3b + 3b ^ 2 = x ^ 3 the solution is: b = -1, x = 1 step by step I calculated that with a software it gives only the solution. Thank you. Last edited by skipjack; September 19th, 2018 at 10:27 AM. September 18th, 2018, 02:54 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 For the second problem, the software didn't find the solution b = 0, x = 1. Last edited by skipjack; September 19th, 2018 at 10:27 AM. September 18th, 2018, 07:24 PM   #3
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Quote:
 Originally Posted by Ak23 how to show that 2n + 1 = x ^ 2 ? the solution is: n = 2 * (2 ^ m-m) x = 1-2 * m and 1 + 3b + 3b ^ 2 = x ^ 3 the solution is: b = -1, x = 1 step by step I calculated that with a software it gives only the solution. thank you.
I think we can simplify this a bit and get rid of the "x", computer or not. If we have $\displaystyle n^2$ then we can get the next square (integer) by adding 2n + 1. ie. $\displaystyle (n + 1)^2 = (n^2) + (2n + 1)$

Similar for the cube:
$\displaystyle (n + 1)^3 = (n^3) + (3n^2 + 3n + 1)$

-Dan September 19th, 2018, 12:15 AM #4 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 @topsquark 2n+1=4n+2 2n-4n=-1 2n=-1 n=-1/2 2.(-1/2)+1 =0 it does not work pair = odd Last edited by Ak23; September 19th, 2018 at 12:17 AM. September 19th, 2018, 03:28 AM #5 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 n=2*(m^2-m) x=1-2*m is solution when z^2=(n+1)^2 y^2=n^2 x^2=2n+1 It's not all numbers only with the squares that is on the odd numbers 1 3 5 7 9 11, .... 2N-1 9 25 49 .... ETC September 19th, 2018, 03:56 AM #6 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 m n x x^2 0 0 1 1 1 0 -1 1 2 4 -3 9 3 12 -5 25 4 24 -7 49 Last edited by Ak23; September 19th, 2018 at 03:59 AM. September 19th, 2018, 05:17 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 If x is odd, it can be written as 1 - 2m. That means that x² = 4m² - 4m + 1 = 2(2m² - 2m) + 1 = 2n + 1, where n = 2(m² - m). If you have no objection, I'll correct your error in the original post, so that the thread can be shortened. Thanks from Ak23 September 19th, 2018, 05:59 AM #8 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 how to find solutions? for x ^ 2 and x ^ 3 September 19th, 2018, 06:34 AM #9 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 Doesn't my previous post show how to find the solutions for x²? Thanks from Ak23 September 19th, 2018, 07:33 AM #10 Newbie   Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 yes I understood thank you very much Tags show Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mared Geometry 7 May 16th, 2015 09:50 PM Few_But_Ripe Complex Analysis 1 November 11th, 2011 09:08 AM notnaeem Real Analysis 4 August 16th, 2010 12:32 PM naserellid Algebra 2 August 15th, 2010 02:20 AM

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