Little math problems September 2018
09-25-2018, 02:46 AM
Post: #10
 Albert Chan Senior Member Posts: 2,516 Joined: Jul 2018
RE: Little math problems September 2018
(09-20-2018 02:37 PM)Albert Chan Wrote:  Edit: found the general form of sum of 2 squares a cube. Not sure if it cover all cases ...

It only take 1 counter-example to dis-prove a conjecture ...

3430000^2 + 10290000^2 = 49000^3 proved the pattern (2 N^3, 2 N^3), (N^3, 2 N^3) were wrong.

This counter-example also proved above link does not cover all cases for two squares sum to a cube:

(A^3 - 3 A B^2)^2 + (3 A^2 B - B^3)^2 = (A^2 + B^2)^3

Searching all integers A, B, 0 <= A <= B, and A^2 + B^2 = 49000, we have 2 solutions.

A, B = 70 , 210 ---> 6174000^2 + 8918000^2 = 49000^3
A, B = 126, 182 --> 2639728^2 + 10520496^2 = 49000^3

Since it is unable to generate the counter-example, the formula does not cover all cases.
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 Messages In This Thread Little math problems September 2018 - pier4r - 09-20-2018, 11:21 AM RE: Little math problems September 2018 - Thomas Klemm - 09-20-2018, 12:54 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 01:03 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 02:37 PM RE: Little math problems September 2018 - Albert Chan - 09-25-2018 02:46 AM RE: Little math problems September 2018 - ijabbott - 09-20-2018, 04:55 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 05:22 PM RE: Little math problems September 2018 - Valentin Albillo - 09-24-2018, 12:53 AM RE: Little math problems September 2018 - Albert Chan - 09-24-2018, 12:18 PM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 12:48 AM RE: Little math problems September 2018 - Albert Chan - 09-28-2018, 04:51 PM RE: Little math problems September 2018 - pier4r - 09-25-2018, 10:56 AM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 04:09 PM RE: Little math problems September 2018 - pier4r - 09-26-2018, 03:55 PM RE: Little math problems September 2018 - Valentin Albillo - 09-26-2018, 08:13 PM RE: Little math problems September 2018 - Albert Chan - 09-26-2018, 10:20 PM RE: Little math problems September 2018 - pier4r - 09-28-2018, 01:36 PM RE: Little math problems September 2018 - pier4r - 09-27-2018, 10:42 PM RE: Little math problems September 2018 - Albert Chan - 09-27-2018, 11:45 PM

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