Hi Frank,
Thanks for the link; it's very informative.
I found that in this particular scenario (i.e., when determinant is perfect square), Reduce factorizes the RHS which, in this case, is the prime number itself (2^n - 1). Since I'm using this equation to factorize the prime number, I can't use this algorithm.
I was hoping something similar to the solution to Pell's equation which indeed is used by Reduce in other cases (when determinant is not a perfect square).
If you are aware of any other algo to solve this equation, please do let me know.
Accept my gratitude in advance.
manoj