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any two cubic number that when added toghether gives anothere cubic number a^3+b^3=c^3. find a,b&c

  • math -

    No, your premise is not true.

    2^3+3^2= a^3
    35, and 35 is not a cube of a natural number.

  • math -

    Fermat's Last Theorem states that there are no solutions to x^n + y^n = z^n for n = 3 or greater. Surprisingly, there are solutions to x^n + y^n = z^(n+1) or z^(n-1).

    1--Divide through by z^n resulting in (x/z)^n + (y/z)^n = z.
    2--Let (x/z) and (y/z) be any positive numbers other than 1.
    3--Solve for z and then x and y.
    4--Example: x^3 + y^3 = z^4
    5--Let (x/z) = 2 and (y/z) = 5. Then 2^3 + 5^3 = 133 = z.
    6--Then x = 2(133) = 266 and y = 5(133) = 665.
    7--Checking: 266^3 + 665^3 = 18,821,096 + 294,079,625 = 312,900,721 = 133^4.
    It works for any n and (n+1).

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