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apple_pi Group Title

51a+2b=84c How to find smallest solutions for a,b,c

  • one year ago
  • one year ago

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  1. apple_pi Group Title
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    @ParthKohli any ideas?

    • one year ago
  2. ParthKohli Group Title
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    Diophantine equations. Gotta hate them.

    • one year ago
  3. sauravshakya Group Title
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    I dont think the question is complete

    • one year ago
  4. ParthKohli Group Title
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    Well, do you need positive integer solutions?

    • one year ago
  5. apple_pi Group Title
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    Yep. Smallest positive

    • one year ago
  6. ParthKohli Group Title
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    Oh yeah, how do you define smallest \(a,b,c\)?

    • one year ago
  7. apple_pi Group Title
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    a b c are integers. no common factors

    • one year ago
  8. sauravshakya Group Title
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    did u mean a+b+c to be smallest

    • one year ago
  9. apple_pi Group Title
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    that also works

    • one year ago
  10. ParthKohli Group Title
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    Oh, you need coprime a,b,c.

    • one year ago
  11. apple_pi Group Title
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    yep

    • one year ago
  12. sauravshakya Group Title
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    Can someone explain me what the real question is?

    • one year ago
  13. apple_pi Group Title
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    what is the smallest amounts of 51 and 2 required to make a multiple of 84

    • one year ago
  14. ParthKohli Group Title
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    lol, I have \(a = b = c= 0\). ;-)

    • one year ago
  15. apple_pi Group Title
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    perhaps I should have mentioned positive :D

    • one year ago
  16. sauravshakya Group Title
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    51*2 + 2*33=84*2

    • one year ago
  17. apple_pi Group Title
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    Oh wait...I did

    • one year ago
  18. ParthKohli Group Title
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    @sauravshakya Nailed it.

    • one year ago
  19. sauravshakya Group Title
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    Note: a must be even

    • one year ago
  20. Callisto Group Title
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    smallest amount of 52 // smallest amount of 2 // small amount of 52 and 2?

    • one year ago
  21. ParthKohli Group Title
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    \[51a + 2b \equiv 0\pmod{84}\]So yup, \(a\) can't be odd.

    • one year ago
  22. Callisto Group Title
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    That means smallest a / smallest b/ smallest c / smallest a+b ?

    • one year ago
  23. apple_pi Group Title
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    8(51)+6(2) = 5(84)

    • one year ago
  24. sauravshakya Group Title
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    So u want to find minimum value of a+b+c???

    • one year ago
  25. apple_pi Group Title
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    yes

    • one year ago
  26. ParthKohli Group Title
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    But they aren't coprime. :-\

    • one year ago
  27. apple_pi Group Title
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    Oh whoops, then I didn't mean coprime As in like a,b,c don't have any common factors across the three of them

    • one year ago
  28. apple_pi Group Title
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    It's all good then guys :D

    • one year ago
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