Merge pull request matthewsamuel95#37 from stuxxnet42/master

added a program to calculate the modular multiplicative inverse

Math/modular_multiplicative_inverse/mmi.cpp

@@ -0,0 +1,48 @@
+/*computes the modular multiplicative inverse:
+ * let x,n be any positive integers
+ * we want to compute m so that:
+ * (m*x)%n=1
+ * i.e. the multiplicative inverse mod n
+ */
+
+#include <iostream>
+
+int inverse(int x, int n){
+    int t=0;
+    int r=n;
+    int newt=1;
+    int newr=x;
+    while(newr!=0){
+        int quot=r/newr;
+        int tmp=newt;
+        newt=t-quot*newt;
+        t=tmp;
+        tmp=newr;
+        newr=r-quot*newr;
+        r=tmp;
+    }
+    if(r>1){
+        return -1;
+    }
+    if(t<0){
+        t+=n;
+    }
+    return t;
+}
+
+
+int main(int argc, char** argv){
+    if(argc!=3){
+        std::cout<<"usage is: mmi x n\nwhere x denotes the given number and n denotes the mod"<<std::endl;
+        return -1;
+    }
+    int x=std::stoi(argv[1]);
+    int n=std::stoi(argv[2]);
+    int result=inverse(x,n);
+    if(result==-1){
+        std::cout<<"not invertible"<<std::endl;
+        return -1;
+    }
+    std::cout<<"inverse is: "<<result<<std::endl;
+    return 0;
+}