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sg001
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Homework Statement
solve the congruence to the smallest possible modulus.
38x[itex]\equiv[/itex]10 (mod84)
Homework Equations
The Attempt at a Solution
Ok so I thought I knew how to do these but apparently not.
So I start out by
38x+84y = 10
Now I think I should find the gcd so I can simplify
so
84 = 38(2) + 8[itex]\Rightarrow[/itex] 8= 84 - 38(2)
38= 8(4) + 6 [itex]\Rightarrow[/itex] 6= 38 - 8(4)
8 = 6(1) + 2 [itex]\Rightarrow[/itex] 2 = 8 - 6(1)
6 = 2(3) + 0 [itex]\Leftrightarrow[/itex] gcd = 2
so 19x + 42y = 5
but then where? I seem to get lost at this point?