Question

51a+2b=84c

How to find smallest solutions for a,b,c

Answer 1

@ParthKohli any ideas?

Answer 2

Diophantine equations.
Gotta hate them.

Answer 3

I dont think the question is complete

Answer 4

Well, do you need positive integer solutions?

Answer 5

Yep. Smallest positive

Answer 6

Oh yeah, how do you define smallest \(a,b,c\)?

Answer 7

a b c are integers. no common factors

Answer 8

did u mean a+b+c to be smallest

Answer 9

that also works

Answer 10

Oh, you need coprime a,b,c.

Answer 11

yep

Answer 12

Can someone explain me what the real question is?

Answer 13

what is the smallest amounts of 51 and 2 required to make a multiple of 84

Answer 14

lol, I have \(a = b = c= 0\). ;-)

Answer 15

perhaps I should have mentioned positive :D

Answer 16

51*2 + 2*33=84*2

Answer 17

Oh wait...I did

Answer 18

@sauravshakya Nailed it.

Answer 19

Note: a must be even

Answer 20

smallest amount of 52 // smallest amount of 2 // small amount of 52 and 2?

Answer 21

\[51a + 2b \equiv 0\pmod{84}\]So yup, \(a\) can't be odd.

Answer 22

That means smallest a / smallest b/ smallest c / smallest a+b ?

Answer 23

8(51)+6(2) = 5(84)

Answer 24

So u want to find minimum value of a+b+c???

Answer 25

yes

Answer 26

But they aren't coprime. :-\

Answer 27

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

Answer 28

It's all good then guys :D