Assignment II

1. Read two integers n and m as input. Output the value of n^m without using the math library. Test your program with the following imputs: n=1, m=0; n=2, m=10; n=5, m=6.
   
   
2. Read two integers n and m as input. Print the table of n starting from n*1 to n*m. So, if you have n=5 and m=10 as your inputs then your program should output

   5 
   10 
   15 
   20
   25
   30
   35
   40
   45
   50
   

3. Read an integer n as input. Check whether n is prime or not? Your program should output "n is PRIME" or "n is NON-PRIME" as the case may be. For instance if the input is 7, your program should print: 7 is PRIME
   
   
   BONUS QUESTIONS (not to be evaluated as a component of this assignment)
   
   
4. Write a C program to print out all Armstrong numbers between 1 and 500. If sum of the cubes of each digit of the number is equal to the number itself, then the number is called an Armstrong number. For example, 153 = ( 1 * 1 * 1 ) + ( 5 * 5 * 5 ) + ( 3 * 3 * 3 ).
5. Write a C program to calculate the sum of all members of the arithmetic progression that contains 999 numbers beginning with -31. The difference of the progression is 7. Your program must obtain the result by direct summation. Then check the computed result using a general formula for the sum of an arithmetic progression.
6. Write a C program that finds the largest among all the numbers upto the last input. The user has the flexibility to input the number one by one without any restriction. He/she can stop to input numbers at any time pressing a special key. Each time, a new number is read, the output displays the maximum upto that point.

   Sample output
   -------------
   Enter a number: 5
   output: MAX is 5
   DO U WANT TO QUIT (Type 0 to quit, 1 to continue): 1
   Enter a number:3
   output: MAX is 5
   DO U WANT TO QUIT (Type 0 to quit, 1 to continue): 1
   Enter a number:10
   output: MAX is 10
   DO U WANT TO QUIT (Type 0 to quit, 1 to continue): 0
   

7. Read an integer n as input. Write a C progam to find all the prime factors of n. Hint: You might use the program for finding prime numbers that you wrote as a part of this assignment to solve this problem.
8. The system of integers modulo 11, written Z/11, is a finite algebraic system consisting of the symbols 0, 1, 2, ... 10. Addition of a and b is defined by the rule "add a and b, then divide by 11 and take the remainder." Thus 5 + 9 ≡ 3 mod 11. Multiplication is defined by the rule "multiply a and b, then divide by 11 and take the remainder." Thus 2 * 9 ≡ 7 mod 11. Write a C program to compute the addition and multiplication tables for Z/11. For example the addition table should look like:

   + 0 1 2 3 4 5 6 7 8 9 10
   0 0 1 2 3 ...
   1 1 2 3 4 ...
   2 2 3 4 5 ...
   3 3 4 5 6 ...
   .
   .
   .
   10 10 0 1 2 ...