System of 3 linear congruences I read this subject and I have doubts.
- Why $x\equiv 25 \pmod{7^2} \implies x\equiv 4\pmod {7} $ ?
$x\equiv 399\pmod{1089}$ Is equivalent to system: $x \equiv 399 \pmod{11^2}; \ \ \ x \equiv 399 \pmod {3^2} $
Is it true that: $$\begin{cases} x\equiv 39 \mod(189) \\ x\equiv 25 \mod(539) \\ x\equiv 399 \mod(1089) \end{cases} \iff \begin{cases}x\equiv 39\pmod{3^3}\\ x\equiv 39\pmod{7}\\ x\equiv 25\pmod{11} \\ x\equiv 25\pmod{7^2}\\ x\equiv 399\pmod{11^2} \\ x\equiv 399\pmod{3^2} \end{cases} $$