Question3. Use CRT to solve the following system of linear congruences: $$\begin{aligned} 2 x & =5(\bmod 7) \\ 4 x & =2(\bmod 6) \\ x & =3(\bmod 5) \end{aligned}$$ (Hint: First determine how many unique solutions modulo 210 exist. Why?)

Studdy Solution
Verify the solution:
- Check $x \equiv 6 \pmod{7}$: $68 \equiv 6 \pmod{7}$ - Check $x \equiv 2 \pmod{3}$: $68 \equiv 2 \pmod{3}$ - Check $x \equiv 3 \pmod{5}$: $68 \equiv 3 \pmod{5}$
All checks are correct. Therefore, the solution is $x \equiv 68 \pmod{210}$.