Lot's of small changes to math chapter.

1 files changed, 17 insertions, 0 deletions

diff --git a/math/legendre.cpp b/math/legendre.cpp
new file mode 100644
index 0000000..adfd3c6
--- /dev/null
+++ b/math/legendre.cpp
@@ -0,0 +1,17 @@
+int legendre(ll a, ll p) {
+  a %= p;
+  if (a == 0) return 0;
+  if (a == 1 || p == 2) return 1;
+  if (a == 2) return (((p * p - 1) / 8) & 1) ? -1 : 1;
+  if (isPrime(a)) {
+    return legendre(p, a) * ((((p - 1) * (a - 1) / 4) & 1) ? -1 : 1);
+  } else {
+    map<ll, int> facts;
+    factor(a, facts);
+    int res = 1;
+    for (auto f : facts)
+      if (f.second & 1)
+        res *= legendre(f.first, p);
+    return res;
+  }
+}