A117318 Numbers n such that Phi(n,x) is a flat cyclotomic polynomial of order four.

431985, 757335, 865365, 1134915, 1296885, 1297815, 1675365, 1729335, 1891815, 2161785, 2162715, 2595165, 2648715, 2649585, 3027165, 3028035, 3132015, 3133785, 3347985, 3405615, 3565785, 3784065, 3891585, 4698465, 4920285, 5188935, 5189865, 5676315

Offset: 1

Author

T. D. Noe, Mar 07 2006

Keywords

• nonn

Comments

A flat polynomial is defined to be a polynomial whose coefficients are -1, 0, or 1. Order four means that n is the product of four odd primes p

For pqrs to be flat, it appears that three conditions on p < q < r < s are required: q = -1 (mod p), r = +-1 (mod pq), and s = +-1 (mod pqr). [T. D. Noe, Apr 13 2010]

Links

• T. D. Noe, Table of n, a(n) for n=1..216
• Nathan Kaplan, Flat cyclotomic polynomials of order four and higher, #A30, Integers 10 (2010), 357-363.
• Carlo Sanna, A Survey on Coefficients of Cyclotomic Polynomials, arXiv:2111.04034 [math.NT], 2021.

Crossrefs

Cf. A117223 (third-order flat cyclotomic polynomials).

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