Suppose that x is an integer that satisfies the following congruences
\(:\begin{align*} 3+x &\equiv 2^2 \pmod{3^3} \\ 5+x &\equiv 3^2 \pmod{5^3} \\ 7+x &\equiv 5^2 \pmod{7^3} \end{align*}\)
What is the remainder when x is divided by 105?
(3 + x) mod 3^3 = 2^2 (5 + x) mod 5^3 = 3^2 (7 + x) mod 7^3 = 5^2, solve for x
Using CRT + MMI, we have:
x = 1157625 n + 506629, where n =0, 1, 2, 3........etc.
The smallest x = 506629
506629 mod 105 == 4
