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 Quarting the cube (Posted on 2013-02-28)

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)

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 computer exploration shows likely true -- no proof | Comment 1 of 6

list
10      cls
20      point 20
40      loop
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       0Break 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

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