A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
51a+2b=84c
How to find smallest solutions for a,b,c
anonymous
 3 years ago
51a+2b=84c How to find smallest solutions for a,b,c

This Question is Closed

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I dont think the question is complete

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0did u mean a+b+c to be smallest

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Can someone explain me what the real question is?

anonymous
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0lol, I have \(a = b = c= 0\). ;)

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

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

Callisto
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0That means smallest a / smallest b/ smallest c / smallest a+b ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So u want to find minimum value of a+b+c???

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

anonymous
 3 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's all good then guys :D
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.