On the Difference in Values of the Euler Totient Function Near Prime Arguments

Stephan Ramon Garcia () and Florian Luca ()
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Stephan Ramon Garcia: Pomona College, Department of Mathematics
Florian Luca: University of the Witwatersrand, School of Mathematics

A chapter in Irregularities in the Distribution of Prime Numbers, 2018, pp 69-96 from Springer

Abstract: Abstract We prove unconditionally that for each ℓ ⩾ 1 $$\ell \geqslant 1$$ , the difference φ(p − ℓ) − φ(p + ℓ) is positive for 50% of odd primes p and negative for 50%.

Date: 2018
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DOI: 10.1007/978-3-319-92777-0_4

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