anonymous
  • anonymous
51a+2b=84c How to find smallest solutions for a,b,c
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@ParthKohli any ideas?
ParthKohli
  • ParthKohli
Diophantine equations. Gotta hate them.
anonymous
  • anonymous
I dont think the question is complete

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ParthKohli
  • ParthKohli
Well, do you need positive integer solutions?
anonymous
  • anonymous
Yep. Smallest positive
ParthKohli
  • ParthKohli
Oh yeah, how do you define smallest \(a,b,c\)?
anonymous
  • anonymous
a b c are integers. no common factors
anonymous
  • anonymous
did u mean a+b+c to be smallest
anonymous
  • anonymous
that also works
ParthKohli
  • ParthKohli
Oh, you need coprime a,b,c.
anonymous
  • anonymous
yep
anonymous
  • anonymous
Can someone explain me what the real question is?
anonymous
  • anonymous
what is the smallest amounts of 51 and 2 required to make a multiple of 84
ParthKohli
  • ParthKohli
lol, I have \(a = b = c= 0\). ;-)
anonymous
  • anonymous
perhaps I should have mentioned positive :D
anonymous
  • anonymous
51*2 + 2*33=84*2
anonymous
  • anonymous
Oh wait...I did
ParthKohli
  • ParthKohli
@sauravshakya Nailed it.
anonymous
  • anonymous
Note: a must be even
Callisto
  • Callisto
smallest amount of 52 // smallest amount of 2 // small amount of 52 and 2?
ParthKohli
  • ParthKohli
\[51a + 2b \equiv 0\pmod{84}\]So yup, \(a\) can't be odd.
Callisto
  • Callisto
That means smallest a / smallest b/ smallest c / smallest a+b ?
anonymous
  • anonymous
8(51)+6(2) = 5(84)
anonymous
  • anonymous
So u want to find minimum value of a+b+c???
anonymous
  • anonymous
yes
ParthKohli
  • ParthKohli
But they aren't coprime. :-\
anonymous
  • anonymous
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
anonymous
  • anonymous
It's all good then guys :D

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