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Euler's Favorite Proof Meets a Theorem of Vantieghem

Summary This article may be regarded as a connection between the past and the present. In 2008 E. Vantieghem proved a new primality criterion whose proof requires the use of cyclotomic polynomials. Almost two and a half centuries ago, Euler used a not-so-well-known method of proof to prove Fermat's little theorem. In this article we show that Euler's method can be adopted in order to prove Vantieghem's result in a more elementary way.