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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

2019

City University of New York (CUNY)

Distribution of primes

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Full-Text Articles in Physical Sciences and Mathematics

Squarefree Totients P-1 And Primitive Roots, Nelson A. Carella Apr 2019

Squarefree Totients P-1 And Primitive Roots, Nelson A. Carella

Publications and Research

This note determines an effective asymptotic formula for the number of squarefree totients $p-1$ with a fixed primitive root t u 6= ±1, v2


Results For Nonwieferich Primes, Nelson A. Carella Apr 2019

Results For Nonwieferich Primes, Nelson A. Carella

Publications and Research

Let $v\geq 2$ be a fixed integer, and let $x \geq 1$ be a large number. The exact asymptotic counting function for the number of nonWieferich primes $p\leq x$ such that $ v^{p-1}-1 \equiv 0 \bmod p^2$ in the interval $[1,x]$ is proposed in this note. The current results in the literature provide lower bounds, which are conditional on the $abc$ conjecture or the Erdos binary additive conjecture.