The irreducibility conjecture for Fekete polynomials at semiprime indices

Let $p$ and $q$ be distinct odd primes and set $n=pq$. Let $f_n$ and $g_n$ denote the reciprocal Fekete polynomial and its trace polynomial, respectively. Semiprime Fekete irreducibility conjecture. Both $f_n$ and $g_n$ are irreducible.

The paper gives an irreducibility criterion using irreducibility of the trace polynomial and an odd count of factors of a fixed degree modulo a prime, and demonstrates the method for $n=15$. The asserted simultaneous irreducibility for every product of two distinct odd primes remains open in the supplied text.