Added definition of quadratic residue. TODO: It is defined for primes only, consider...

diff --git a/numbertheory.txt b/numbertheory.txt
index 23db6de..db521a3 100644 (file)
--- a/numbertheory.txt
+++ b/numbertheory.txt
@@ -9,6 +9,34 @@ type Exp    = ℕ[M];
 type Result = ℕ[N^M];
 type nat    = ℕ[K];
 
+// Elementary division
+pred divides(m:nat,n:nat) ⇔ ∃p:nat. m*p = n;
+
+// Quadratic residue
+// a ∈ ℤ/pℤ is a quadratic residue ⇔
+// x^2 - a has a zero in ℤ/pℤ
+// defined for p prime > 2 only
+proc isquadraticresidue(a:nat,p:nat): Bool
+{
+   var res:Bool = false;
+   var i:nat = 0;
+
+   while i < p ∧ res = false do
+   {
+      if (i^2-a)%p = 0 then
+         res = true;
+      i = i+1;
+   }
+
+   return res;
+}
+
+// Legendre Symbol   (a/p)
+// ==  0   divides(p,a)
+// ==  1   a is quadratic residue modulo p
+// == -1   a is NOT quadratic residue modulo p
+
+
 ////////////////////////////////////////////////////////////////////
 // Algorithm: Calcluate Integer Root of a
 // See http://www.inf.fh-flensburg.de/lang/se/veri/aufg/wurzel.htm
@@ -97,3 +125,4 @@ proc main(): ()
 
 
 
+