Find all integers x that satisfy the following system of congruences:
9x≡1(mod 20) ; 52x≡2 (mod 209) ; 8x≡(mod 21)
need elaborate and quick answers please
First, find the prime factorization for each: Then, consider mod 4 and mod 5 (this will allow you to easily calculate mod 4 and mod 5). Then consider mod 11 and mod 19 to calculate mod 11 and mod 19. Finally, consider mod 3 and mod 7 to calculate mod 3 and mod 7. Once you know mod 4, 5, 11, 19, 3, and 7, use the Chinese Remainder Theorem to find mod .