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  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
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 2n4n=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^2m) x=12*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, .... 2N1 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. 
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?

September 19th, 2018, 07:33 AM  #10 
Newbie Joined: Sep 2018 From: tunis Posts: 27 Thanks: 0 
yes I understood thank you very much


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