Chinese Remainder Theorem

[morrowcosom]

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

Find a satisfying a 1 (mod 2), a 2 (mod 3), with 0 < a < 6

Begin with the Mod 2 calculation




2. Relevant equations



3. The attempt at a solution

I found that U1=3 and U2=4, but then it says "Now take the appropriate linear combination of {U1, U2} to find a which matches the required congruences: a 1 (mod 2), a 2 (mod 3)".

How do take the appropriate linear combination of 3 and 4 to find a? (I know the answer is 5 just by looking at it, but have no idea how to get there via the method mentioned above)

Thanks for the help