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April 10th, 2018, 08:27 AM   #1
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ax+by=c equation, and numeric system problem.

We have the equation:
(E):5x-6y=3

1-Solve 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 3-base system.
b=αβ0α in the 5-base system.

-Find α and β , knowing that (a,b) is a solution to (E)

Help please with the last question.
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April 10th, 2018, 09:29 AM   #2
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(α, β) = (2, 4)
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April 10th, 2018, 10:16 AM   #3
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Quote:
Originally Posted by skipjack View Post
(α, β) = (2, 4)
But how?
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April 10th, 2018, 10:41 AM   #4
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Trial and error. There are only three possibilities for the value of α, of which only α = 2 leads to a solution.
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April 10th, 2018, 10:46 AM   #5
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Quote:
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Trial and error. There are only three possibilities for the value of α.
Actually it's just 2, but I'm looking for a mathematical way to solve, thanks anyway.
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April 10th, 2018, 02:53 PM   #6
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What does solving in Z^2 mean?
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April 10th, 2018, 04:31 PM   #7
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What does solving in Z^2 mean?
I'll give you the (very) simple run-down. $\displaystyle \mathbb{Z} ^2$ is the set of all ordered pairs (a, b) where a and b are both integers.

-Dan
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