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Lemma: Möbius and Floor Functions Combined

For every real number $x \ge 1$ we have: $$\sum_{n=1}^{\lfloor x\rfloor}\mu(n)\left\lfloor\frac xn\right\rfloor=1.$$

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Proofs: 1 Explanations: 1

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References

Bibliography

  1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
  2. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927