The number of cross-join pairs in maximum length linear sequences

It has been conjectured by T. Chang et al. (1990) that the number of cross-join pairs in a maximum length linear sequence equals (2^n-1-1)(2^n-1-2)/6. A maximum length linear sequence (an m-sequence) of length 2ⁿ-1 is a binary sequence which satisfies a linear recurrence whose characteristic polynomial is primitive of degree n. The number of primitive polynomials is given by φ(2ⁿ-1)/n, where φ is Euler´s φ-function. A proof of the conjecture is given