A specific family of cyclotomic polynomials of order three (Q625836)

The \(n\)-th cyclotomic polynomial \(\Phi_{n}(x)\) is called flat if the largest absolute value of its coefficients is \(1\). Let \(p<q<r\) be odd primes and \(2r\equiv\pm 1\pmod{pq}\). The author proves that \(\Phi_{pqr}(x)\) is flat if and only if \(p=3\) and \(q\equiv 1\pmod p\).