From https://en.m.wikipedia.org/wiki/Chinese_remainder_theorem
Let $n_1, ..., n_k$ be integers greater than 1, which are often called moduli or divisors. Let us denote by $N$ the product of the $n_i$.
The Chinese remainder theorem asserts that if the $n_i$ are pairwise coprime, and if a1, ..., ak are integers such that $0 ≤ a_i < n_i$ for every $i$, then there is one and only one integer $x$, such that $0 ≤ x< N$ and the remainder of the Euclidean division of $x$ by $n_i$ is $a_i$ for every $i$.
This may be restated as follows in term of congruences: If the $n_i$ are pairwise coprime, and if $a_1, ..., a_k$ are any integers, then there exist integers $x$ such that
$${\displaystyle {\begin{aligned}x&\equiv a_{1}{\pmod {n_{1}}}\\&\,\,\,\vdots \\x&\equiv a_{k}{\pmod {n_{k}}},\end{aligned}}}{\displaystyle {\begin{aligned}x&\equiv a_{1}{\pmod {n_{1}}}\\&\,\,\,\vdots \\x&\equiv a_{k}{\pmod {n_{k}}},\end{aligned}}}$$
I understood few things, like when x is divided by a divisor ($n_1$) then the remainder is $a_1$, so $x=kn_1+a_1$
But I'm having trouble "reading" the statement, and understanding in the present format. I visited Wikipedia because I have literally no knowledge in modular arithmetic, I don't even know the basic terms. I was hoping Wikipedia would help but it's not helping.
Any website(not YouTube) where I could I learn about these terms at one place?
$x\equiv y \mod n$ means $(x-y)/n \in \Bbb Z.$
This is almost always in a context where $x,y,n \in \Bbb Z$ (and usually $n>0$ ), where it means $n$ is a divisor of $x-y,$ that is, $x$ and $y$ have the same remainder when divided by $n.$
The basic tools, for integers, with $n>0,$ are:
There is exactly one integer $a'$ with $a'\equiv a \mod n$ and $0\le a'\le n-1.$
$a\equiv a'\mod n \iff a-a'\equiv 0 \mod n.$
If $a\equiv a'$ & $b\equiv b'$ & $c\equiv c' \mod n$ then $ab+c\equiv a'b'+c' \mod n.$
If $a\equiv b \mod n$ and if $m\in \Bbb Z^+$ then $a^m\equiv b^m \mod n.$