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arXiv · 1706.00392

On the difference in values of the Euler totient function near prime arguments

Stephan Ramon Garcia·Florian Luca
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Abstract

We prove unconditionally that for each $\ell \geq 1$, the difference $\phi(p-\ell) - \phi(p+\ell)$ is positive for $50\%$ of odd primes $p$ and negative for $50\%$.

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Stephan Ramon Garcia, Florian Luca. 2017-06-01. On the difference in values of the Euler totient function near prime arguments. https://arxiv.org/abs/1706.00392

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