In Chapter 5 we studied Euler’s function φ. Two of its most important properties are Theorem 5.6, that if m and n are coprime then φ(mn) = φ(m)φ(n), and Theorem 5.8, that ∑ d/n ø(d) = n for all n. In this chapter we will meet other examples of functions with similar properties. Some of these, such as the divisor functions and the Möbius function, have important applications, including the study of perfect numbers and various enumeration problems.
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