All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Quarting the cube (Posted on 2013-02-28) Difficulty: 3 of 5

Select integer x and triangular number y such that 8y=3x^4-2x^2-1.

Prove that y is divisible by 28 - or find a counter-example.

See The Solution Submitted by broll    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer exploration shows likely true -- no proof | Comment 1 of 6


list
   10      cls
   20      point 20
   30      Addend=1
   40      loop
   50          Y=Y+Addend:inc Addend
   60          X2=(2+sqrt(4+4*(3*(1+8*Y))))/6
   70          X2r=int(X2+0.5)
   80          if 8*Y=3*X2r^2-2*X2r-1 then
   90           :X=sqrt(X2)
  100           :Ymod28=Y-28*int(Y/28)
  110           :print Y,using(5,20),X,:print Ymod28
  130      endloop


   y                        x                  y mod 28
 28                 3.00000000000000000000       0
 5460              11.00000000000000000000       0
 1059240           41.00000000000000000000       0
 205487128        153.00000000000000000000       0
 39863443620      571.00000000000000000000       0
 7733302575180   2131.00000000000000000000       0
Break in 60

Shows all (x,y) up to (2131,7733302575180) with integral x and triangular y, and all fit the divisibility criterion.


  Posted by Charlie on 2013-02-28 16:51:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information