# Divisibility in arithmetic

1. Apr 25, 2012

### mtayab1994

Chinese remainder theorem help

1. The problem statement, all variables and given/known data

Solve in $$Z^{2}:6x-5y=1$$

Conclude the solution to the system:

X≡2(mod5) , X≡1(mod6)

3. The attempt at a solution

1- solved the equation and found one unique solution which was S={(1,1)}

Given:
X≡2(mod5) , X≡1(mod6)

X≡2(mod5) means X=5t+2

X≡1(mod6) means 5t+2=1(mod6) which is 5t=-1(mod6) But how can i proceed from here on?

Last edited: Apr 25, 2012
2. Apr 25, 2012

Solved it :)