Chapter 2

1.

The function f(n) is defined as follows:

Input a positive integer N and print the value of f(N). The number N may be so large that using an array of N integers is not allowed (as well as an array whose length grows with N).

2.

Find the first positive integer N such that it can be written as a sum of squares of four integers (i.e. N = k² + l² + m² + n² for some integers k,l,m,n) in more than one way.

3.

Input a positive inetger n and fill a two-dimensional array A[n][n] with numbers so that they form a spiral (see Fig. 1).

4.

Print out all four digit positive integers whose digits are all different. Generalize this problem for numbers with n digits.

5.

Given a number N and an integer array A[N] of length N. Write a function that finds the the length of the longest sequence of zeros in the array.