We present a number of classical proofs of the irreducibility of the nth cyclotomic polynomial Φ_n(x). For n prime we present proofs due to Gauss (1801), in both the original and a simplified form, Kronecker (1845), and Sch?nemann/Eisenstein (1846/1850). For general n, we present proofs due to Dedekind (1857), Landau (1929), and Schur (1929).
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