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.
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.
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Posted by Charlie
on 2013-02-28 16:51:58 |
computer exploration shows likely true -- no proof
