Exercise 2

Added Exercise 2 to repository

Informatik_I/Exercise_2/task_3a/README.md

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+# Task
+
+_Fibonacci numbers_ are the integers in the following sequence: $0, 1, 1, 2, 3, 5, 8, 13, 21, ...$. Each number is the sum of the two previous numbers.
+
+_Fibonacci primes_ are Fibonacci numbers that are also prime numbers. Write a program that asks the user for an integer $m$ and then computes and prints all Fibonacci primes between $0$ and $m$ (including). Print each number on a new line.
+
+Finally, on a new line print the total number of Fibonacci primes found.
+
+## Example
+
+If your program is asked to print the Fibonacci primes between $0$ and $14$ the output should look something like this:
+
+```
+2
+3
+5
+13
+Found 4 Fibonacci primes
+```
+
+**Important:** using anything other than `int` (e.g., `unsigned int`, floating point numbers, `long`, or double `long`) is forbidden.

Informatik_I/Exercise_2/task_3a/main.cpp

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+#include <iostream>
+
+int main() {
+  int a = 1;
+  int b = 1;
+  int cnt = 0;   // Initialization of number of deviders
+  int count = 0; // Initialization of number of Fibonacci primes
+  int n = 2;     // Fibonacci number
+  int i = 0;     // Input variable
+
+  std::cin >> i;
+
+  for (; n <= i;) {
+    // Reset counters
+    cnt = 0;
+
+    // Check for deviders of Fibonacci number
+    if (n <= 22360) {
+      for (int j = 1; j <= 22360; ++j) { // 22360 = sqrt(500000000)
+        if (n % j == 0) {
+          ++cnt;
+        }
+      }
+      // Increase count if Fibonacci number is a prime number
+      if (cnt == 2) {
+        std::cout << n << "\n";
+        ++count;
+      }
+    } else if (n > 22360) {
+      for (int j = 1; j <= 22360; ++j) { // 22360 = sqrt(500000000)
+        if (n % j == 0) {
+          ++cnt;
+        }
+      }
+      if (cnt == 1) {
+        std::cout << n << "\n";
+        ++count;
+      }
+    }
+    // Initialize next Fibonacci number
+    a = b;
+    b = n;
+    n = a + b;
+  }
+  // End message
+  std::cout << count << "\n";
+}