Little math problems September 2018

09252018, 02:46 AM
Post: #10




RE: Little math problems September 2018
(09202018 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 counterexample to disprove 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 counterexample 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 counterexample, the formula does not cover all cases. 

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