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I need to cite the classical Zsigmondy Theorem, which was proved in 1892.

Is there any modern reference to this theorem?

I mean some standard textbook in Number Theory containing this theorem together with the proof.

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    $\begingroup$ If you just need to cite the theorem, what's wrong with citing the original source? $\endgroup$
    – Wojowu
    Commented Jun 22, 2020 at 11:13
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    $\begingroup$ In Linear Forms in Logarithms and Applications by Yann Bugeaud, European Mathematical Society, 2018, there are mentions and references on pages 95 and 106 $\endgroup$
    – Yaakov Baruch
    Commented Jun 22, 2020 at 11:28
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    $\begingroup$ I plan to include both the original course and the modern one (for those that do not read German, for example). $\endgroup$
    – Taras Banakh
    Commented Jun 22, 2020 at 11:28

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M. Teleuca, Zsigmondy's theorem and its applications in contest problems, International Journal of Mathematical Education in Science and Technology Volume 44, 2013 - Issue 3, Pages 443-451, https://www.tandfonline.com/doi/abs/10.1080/0020739X.2012.714493?mobileUi=0&journalCode=tmes20

The abstract begins, "In this article, we present a detailed proof of Zsigmondy's theorem."

See also https://math.stackexchange.com/questions/660585/elementary-proof-of-zsigmondys-theorem and Moshe Roitman, On Zsigmondy primes, Proceedings of the American Mathematical Society, Volume 125, Number 7, July 1997, Pages 1913–1919, https://www.ams.org/journals/proc/1997-125-07/S0002-9939-97-03981-6/S0002-9939-97-03981-6.pdf

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    $\begingroup$ There are also notes of Jameson on cyclotomic polynomials. A MathOverflow search should reveal the link. It has a proof following Roitman. Gerhard "My Goto For Cyclotomic Polynomials" Paseman, 2020.06.22. $\endgroup$
    – Gerhard Paseman
    Commented Jun 22, 2020 at 15:15
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Indeed, it is very difficult to find Zsigmondy's theorem with a proof in a book. However, it is proved in Appendix B to Chapter 30 in

Berkovich, Ya. G.; Zhmudʹ, E. M. Characters of finite groups. Part 2. Translated from the Russian manuscript by P. Shumyatsky [P. V. Shumyatskiĭ], V. Zobina and Berkovich. Translations of Mathematical Monographs, 181. American Mathematical Society, Providence, RI, 1999.

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