Prime factors of $\Phi_3(x)$ of the same form

Cody S. Hansen; Pace P. Nielsen

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arXiv · 2204.08971

Prime factors of $\Phi_3(x)$ of the same form

Cody S. Hansen·Pace P. Nielsen

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Abstract

We parameterize solutions to the equality $\Phi_3(x)=\Phi_3(a_1)\Phi_3(a_2)\cdots\Phi_3(a_n)$ when each $\Phi_3(a_i)$ is prime. Our focus is on the special cases when $n=2,3,4$, as this analysis simplifies and extends bounds on the total number of prime factors of an odd perfect number.

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BibTeX RIS

Cody S. Hansen, Pace P. Nielsen. 2022-04-19. Prime factors of $\Phi_3(x)$ of the same form. https://arxiv.org/abs/2204.08971

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