Two conjectures of B. R. Santos concerning totitives

Authors:
H. G. Kopetzky and W. Schwarz

Journal:
Math. Comp. **33** (1979), 841-844

MSC:
Primary 10A20; Secondary 10H25

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521300-8

MathSciNet review:
521300

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Abstract | References | Similar Articles | Additional Information

Abstract: Recently B. R. Santos conjectured that 12 is the largest integer *n* with the following property:

*x*, it is proved that the conjecture of Santos is true. The same result holds, if in addition it is assumed in that

*m*is a prime.

**[1]**E. LANDAU,*Handbuch der Lehre von der Verteilung der Primzahlen*, Teubner, Leipzig und Berlin, 1909.**[2]**J. B. ROSSER & L. SCHOENFELD, "Approximate formulas for some functions of prime numbers,"*Illinois J. Math.*, v. 6, 1962, pp. 64-94. MR**0137689 (25:1139)****[3]**J. B. ROSSER & L. SCHOENFELD,*Sharper Bounds for the Chebyshev Functions**and*, University of Wisconsin MRC Technical Summary Report #1475, 1974.**[4]**B. R. SANTOS, "Twelve and its totitives,"*Math. Mag.*, v. 49, 1976, pp. 239-240. MR**0417037 (54:5098)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521300-8

Keywords:
Prime number theorem,
prime totitives

Article copyright:
© Copyright 1979
American Mathematical Society