The book on Discrete Mathematics by Rosen is really good. A joy to share time with. Very clear explanations. Of the Chinese Remainder Theorem for example. I have a so called "excellent" book on Number Theory from Dover publications in which the CRT seems too difficult to understand by a mortal. Rosen cuts through it right away. Mathematics is always simple once you understand it. Why not keep it simple when communicating it to students?  Anyway. The CRT is an algorithm for solving systems of linear congruence equations. Like for example.
$$
\begin{cases}
x \equiv 1 \bmod{3} \\
x \equiv 2 \bmod{5} \\
x \equiv 3 \bmod{7}
\end{cases}
$$
which has solution $x=52 \bmod{105}$ which can simply be verified like $ 52 \bmod{7} =3$ because $52 = 7.7 + 3$.
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