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April 10th, 2018, 08:27 AM  #1 
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0  ax+by=c equation, and numeric system problem.
We have the equation: (E):5x6y=3 1Solve in Z^2 the equation (I already did, the solution is (x,y)=(6k+3 , 5k+2) (k∈Z)) 2 a and b are natural numbers: a=1α0α00 in the 3base system. b=αβ0α in the 5base system. Find α and β , knowing that (a,b) is a solution to (E) Help please with the last question. 
April 10th, 2018, 09:29 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
(α, β) = (2, 4)

April 10th, 2018, 10:16 AM  #3 
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0  
April 10th, 2018, 10:41 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
Trial and error. There are only three possibilities for the value of α, of which only α = 2 leads to a solution.

April 10th, 2018, 10:46 AM  #5 
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0  
April 10th, 2018, 02:53 PM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 651 Thanks: 86 
What does solving in Z^2 mean?

April 10th, 2018, 04:31 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  

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byc, equation, numeric, problem, system 
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