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 Imperfectly Cubed (Posted on 2013-09-29)
Consider three distinct odd positive integers A, B and C - none of which is a perfect cube.

Can the respective cube roots of A, B and C form three consecutive terms of an arithmetic sequence?

If so, provide an example. If not, prove it.

 No Solution Yet Submitted by K Sengupta No Rating

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 re(4): computer solutioNs ....NOT YET Comment 6 of 6 |

5    point 5
10    for Tot=84 to 999999 step 2
20       for A=1 to int(Tot/2) step 2
30          B=Tot-A
40          Cra=A^(1/3)
50          Crb=B^(1/3)
55            Crarnd=int(Cra+0.5):Crbrnd=int(Crb+0.5)
60          if abs(Cra-Crarnd)>0.000000001 and abs(Crb-Crbrnd)>0.0000000001 and A<>B then
70              :Crc=Crb+Crb-Cra:Crcrnd=int(Crc+0.5)
75              :if abs(Crc-Crsrnd)>0.000000001 then
80              :C=Crc*Crc*Crc
90              :Crnd=int(C+0.5)
100              :if abs(C-Crnd)<0.000000000001 and Crnd@2<>0 then
110                   :print A,B,Crnd:Ct=Ct+1
115                   :if Ct@44=0 then while inkey="":wend:print
120        next A
130     next Tot

`3       81      3755       135     6257       189     8759       243     112511      297     137513      351     16253       375     218715      405     187581      375     102917      459     212519      513     237521      567     26255       625     364523      621     287525      675     3125135     625     171529      783     362531      837     38757       875     510333      891     412535      945     43753       1029    659137      999     4625189     875     240139      1053    487581      1029    39939       1125    656141      1107    512543      1161    537545      1215    562547      1269    5875243     1125    308749      1323    612511      1375    8019375     1029    218751      1377    637553      1431    662555      1485    687557      1539    712513      1625    947759      1593    7375297     1375    377361      1647    76255       1715    10985`

 Posted by Charlie on 2013-09-30 00:28:11

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