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ParthKohli Group Title

Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]

  • one year ago
  • one year ago

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  1. perl Group Title
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    hmmm

    • one year ago
  2. ParthKohli Group Title
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    Can you help me with that?

    • one year ago
  3. perl Group Title
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    find all integer solutions

    • one year ago
  4. perl Group Title
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    looks like we can factor something here

    • one year ago
  5. perl Group Title
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    did you try to expand (a+b+c)^3

    • one year ago
  6. ParthKohli Group Title
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    Whoo.

    • one year ago
  7. ParthKohli Group Title
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    \[a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3\]

    • one year ago
  8. ParthKohli Group Title
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    So do we have to add \(3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2\) to both sides?

    • one year ago
  9. ParthKohli Group Title
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    \[(a + b + c)^3 = 3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2 + 100a + 10b + c \]

    • one year ago
  10. perl Group Title
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    oh look at that

    • one year ago
  11. perl Group Title
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    one second

    • one year ago
  12. perl Group Title
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    (a+b+c)^3 = a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3

    • one year ago
  13. ParthKohli Group Title
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    How would you solve it now?

    • one year ago
  14. perl Group Title
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    not sure

    • one year ago
  15. perl Group Title
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    where did you get this question, is it solvable?

    • one year ago
  16. perl Group Title
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    well the simple approach is , equate terms

    • one year ago
  17. ParthKohli Group Title
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    Yes, a solution is \((1,5,3)\)

    • one year ago
  18. perl Group Title
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    |dw:1360413980599:dw|

    • one year ago
  19. perl Group Title
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    so if a^2 = 100 , b^2 = 10 , and c^2 = 1 , you have a solution

    • one year ago
  20. ParthKohli Group Title
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    I didn't mention that \((a,b,c)\) all must be single-digit numbers.

    • one year ago
  21. perl Group Title
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    ok, then you can go through all the cases , 0-9

    • one year ago
  22. ParthKohli Group Title
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    I want a purely mathematical solution :-|

    • one year ago
  23. ParthKohli Group Title
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    Not by guesses...

    • one year ago
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