On integers not of the form n - φ (n)

Volume 68 / 1995

J. Browkin, A. Schinzel Colloquium Mathematicum 68 (1995), 55-58 DOI: 10.4064/cm-68-1-55-58


W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^k·509203$ (k = 1, 2,...) is of the form n - φ(n).


  • J. Browkin
  • A. Schinzel

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