Problems of the day

1.

Write a Maple program that prints the first 10 squares (i.e. 1², 2², ..., 10²).

2.

Write a Maple program that tests whether two integers are relatively prime.

3.

Write a Maple program that tests whether a number is prime (don't use Maple's built in prime testing procedure).

4.

Check your program from the previous question by comparing it with Maple's isprime function for the first 100 numbers.

5.

Write a program which, given a piece of text, returns the text written backwards.

6.

Write a program which, given a piece of text, returns a list of the characters occurring in the text, along with the number of times they occur, in order of decreasing frequency. (Eg: given ``eep'', would return (e,2), (p,1)).

7.

Write a Maple program which, given an RSA public key [n,a], finds the corresponding private key.