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

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apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0@ParthKohli any ideas?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Diophantine equations. Gotta hate them.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1I dont think the question is complete

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Well, do you need positive integer solutions?

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0Yep. Smallest positive

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Oh yeah, how do you define smallest \(a,b,c\)?

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0a b c are integers. no common factors

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1did u mean a+b+c to be smallest

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, you need coprime a,b,c.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Can someone explain me what the real question is?

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0what is the smallest amounts of 51 and 2 required to make a multiple of 84

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0lol, I have \(a = b = c= 0\). ;)

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0perhaps I should have mentioned positive :D

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0@sauravshakya Nailed it.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Note: a must be even

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.0smallest amount of 52 // smallest amount of 2 // small amount of 52 and 2?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[51a + 2b \equiv 0\pmod{84}\]So yup, \(a\) can't be odd.

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.0That means smallest a / smallest b/ smallest c / smallest a+b ?

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1So u want to find minimum value of a+b+c???

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0But they aren't coprime. :\

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0Oh whoops, then I didn't mean coprime As in like a,b,c don't have any common factors across the three of them

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0It's all good then guys :D
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