Please!
where '=' means 'congruent to'
Solve both system of equations:
1.
x = 0 (mod 2)
x = 0 (mod 3)
x = 1 (mod 5)
x = 6 (mod 7)
Answer: x = ? (mod 210)
2.
x = 0 (mod 4)
x = 1 (mod 9)
x = 2 (mod 25)
x = 3 (mod 49)
Answer: x = ? (mod 44100)
where '=' means 'congruent to'
See here.
2, 3, 5, and 7 are pairwise coprime, so we may apply the Chinese Remainder theorem.
To start the answer, as you mentioned, will be a modulo 2 x 3 x 5 x 7 = 210.
We need to find a set of pairs of integers such that
As example solutions I get
(Any solutions to these equations is acceptable.)
So the solution to the system of equivalences is
You do the second one.
-Dan
Here's a good page on it
Chinese Remainder Theorem/Introductory - AoPSWiki