Let *p < q* be odd primes, and let
denote the maximum of the differences (gaps)
between two consecutive exponents occurring in the *pq*-th
cyclotomic polynomial . In this note, we give an
alternative proof of the following result which was established
by Hong et al. [J. Number Theory, 132 (2012), pp. 2297-2315]

In addition, we show that the number of maximum gaps in is given by .

In addition, we show that the number of maximum gaps in is given by .

Key Words: Cyclotomic polynomial, Binary cyclotomic polynomial, Maximum gap.

2000 Mathematics Subject Classification: Primary: 11C08;

Secondary: 11B83..