A community for students.
Here's the question you clicked on:
 0 viewing
Uniqueartist1
 one year ago
ax + by = cz
where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. The challenge is to either solve that conjecture or come up with a counterexample.
can somebody help me solve this?
Uniqueartist1
 one year ago
ax + by = cz where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. The challenge is to either solve that conjecture or come up with a counterexample. can somebody help me solve this?

This Question is Closed

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.12*10+1*3=1*23 I do not see any common factors since 1 is not a prime.

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1The example I just given may not be very convincing so I will give you another one. Let c=3 since it is a prime. Let x and y be positive integers that is greater than 2 and divisible by 3, say x=6 and y=15. Let a and b be positive integers that are not divisible by 3, say a=2 and b=5. 2*6+5*15=3*z 12+75=3*z 87=3*z z=29 x=6, y=15, z=29, all greater than 2. a=2, b=5, c=3, no common prime factors for all three numbers. In fact, a,b,c are pairwise coprime.
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.