Answer to Question #98936 in Combinatorics | Number Theory for Dorothy

Question

Let f(x) be a function on the set of real numbers x ≥ 1.
Define the function g(x) for x ≥ 1 by
g(x) = X
1≤n≤x
f(x/n).

Prove that
f(x) = X
1≤n≤x
µ(n)g(x/n).

Here µ is the M¨obius function.

Answer 1

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