Rewrite CRT

Author: simonlindholm

content/number-theory/CRT.h

@@ -0,0 +1,23 @@
+/**
+ * Author: Simon Lindholm
+ * Date: 2019-05-22
+ * License: CC0
+ * Description: Chinese Remainder Theorem.
+ *
+ * \texttt{crt(a, m, b, n)} computes $x$ such that $x\equiv a \pmod m$, $x\equiv b \pmod n$.
+ * If $|a| < m$ and $|b| < n$, $x$ will obey $0 \le x < \text{lcm}(m, n)$.
+ * Assumes $mn < 2^{62}$.
+ * Status: Works
+ * Time: $\log(n)$
+ */
+#pragma once
+
+#include "euclid.h"
+
+ll crt(ll a, ll m, ll b, ll n) {
+	if (n > m) swap(a, b), swap(m, n);
+	ll x, y, g = euclid(m, n, x, y);
+	assert((a - b) % g == 0); // else no solution
+	x = (b - a) % n * x % n / g * m + a;
+	return x < 0 ? x + m*n/g : x;
+}

content/number-theory/chapter.tex

@@ -16,6 +16,7 @@ \section{Primality}
 \section{Divisibility}
 	\kactlimport{euclid.h}
 	\kactlimport{Euclid.java}
+	\kactlimport{CRT.h}
 
 	\subsection{Bézout's identity}
 	For $a \neq $, $b \neq 0$, then $d=gcd(a,b)$ is the smallest positive integer for which there are integer solutions to
@@ -29,9 +30,6 @@ \section{Fractions}
 	\kactlimport{ContinuedFractions.h}
 	\kactlimport{FracBinarySearch.h}
 
-\section{Chinese remainder theorem}
-	\kactlimport{chinese.h}
-
 \section{Pythagorean Triples}
  The Pythagorean triples are uniquely generated by
  \[ a=k\cdot (m^{2}-n^{2}),\ \,b=k\cdot (2mn),\ \,c=k\cdot (m^{2}+n^{2}), \]