[math]2^9-1 = 511 = 7 \times 73[/math].
This isn't quite a coincidence. [math]X^{ab}-1[/math] is always divisible by [math]X^a-1[/math], no matter what [math]X[/math] is (it could even be a variable). In this case, [math]9 = 3 \times 3[/math], so [math]2^9-1[/math]must be divisible by [math]2^3-1[/math].
A better question is this: if [math]p[/math]...
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