On integers not of the form n - φ (n)
Tom 68 / 1995
Colloquium Mathematicum 68 (1995), 55-58 DOI: 10.4064/cm-68-1-55-58
W. Sierpiński asked in 1959 (see , pp. 200-201, cf. ) 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).