What next?
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It looks like you can write . Is this what you are aiming for?
No, this section:
As polynomials, you can't factor those anymore.
I have broken it down to but it isn't fully decomp. What to do next?
is congruent to mod 3, according as n is even or odd. So is a multiple of 3. In fact it is equal to 3*87211, and 87211 is prime, as you can check here.