Assignment 2

Write a program to determine the two positive integers with properties described below:

Part I

Find the smallest positive integer n with the following property. Let n = a_ka_k-1...a₁a₀ be the decimal expansion of n with a_k > 0. Look at the integer n_r = a₀a_ka_k-1...a₂a₁ (the cyclic right shift of n). The desired property of n is that n_r must be a proper integral multiple of n. Also report the multiplier n_r/n.

Part II

Find the smallest positive integer n with the following property. Let n = a_ka_k-1...a₁a₀ be the decimal expansion of n with a_k > 0. Look at the integer n_l = a_k-1a_k-2...a₁a₀a_k (the cyclic left shift of n). The desired property of n is that n_l must be a proper integral multiple of n. Also report the multiplier n_l/n.

Note: Write a single program. Use integer arithmetic only. Since integers cannot be arbitrarily large in C, report "failure" if your program fails to locate the desired value(s) of n after checking all n <= 10⁹. There is no need to use arrays for solving this assignment. However, there is no penalty if you use them.

b is called a proper multiple of a, if b = ka for some integer k > 1.

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