(1) The following function is a function often used as a simple random number generator.
where is a non-negative integer and denotes a modulus operator (the remainder).
Write a program that computes for given . Then print the value of by using this program.
(2) Write a program that counts the number of such that and is an even number.
(3) Write a program that counts the number of such that is an odd number, , and is an even number.
(4) Write a program that prints the value of .
(5) Write a program that computes the following function where is a non-negative integer:
Then run the program to print the values of and .
(6) Write a program that computes the smallest positive integer such that for any non-negative integer .
(7) Write a program that computes the smallest positive integer such that for any non-negative integer . Write on the answer sheet why the program correctly computes . is a function defined as follows: