diff --git a/Fermat_Little_Theorem/Fermat_Little_Theorem.java b/Fermat_Little_Theorem/Fermat_Little_Theorem.java
new file mode 100644
index 0000000000..59d3e7584e
--- /dev/null
+++ b/Fermat_Little_Theorem/Fermat_Little_Theorem.java
@@ -0,0 +1,56 @@
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStreamReader;
+
+/*
+x^(n-1) cong== 1modn
+where x and n are coprime (gcd is 1)
+multiplying by x inverse on both sides
+x inverse = x^(n-2) mod n which is found using fast modular exponentiation
+ */
+public class Fermat_Little_Theorem {
+    public static void main(String[] args) throws IOException {
+        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+        int x;
+        int n;
+        System.out.println("Enter space separated coprime numbers x and n");
+        String input[] = br.readLine().split(" ");
+        x = Integer.parseInt(input[0]);
+        n = Integer.parseInt(input[1]);
+        findModInverse(x,n);
+    }
+    public static void findModInverse(int x, int n){
+
+        if(recursiveGCD(x,n)!=1){
+            System.out.println("inverse does not exist! returning...");
+            return;
+        }
+        else{
+            System.out.println("Modular Multiplicative inverse is..."+ fastModuloExponentiation(x,n-2,n));
+        }
+
+
+    }
+    public static int recursiveGCD(int a, int b){
+        return a==0 ? b:recursiveGCD(b%a,a);
+    }
+
+    public static long fastModuloExponentiation(int number, int power, int modulus){
+        if(power==0)
+            return 1;
+        if(power==1)
+            return number;
+        long sub_number = fastModuloExponentiation(number,power/2,modulus)%modulus;
+        if(power%2==0)
+            return (sub_number*sub_number)%modulus;
+        else
+            return ((sub_number*sub_number)%modulus * number%modulus)%modulus;
+    }
+}
+
+/*
+input :
+3 11
+output :
+Modular Multiplicative inverse is...4
+ */
\ No newline at end of file