further refinement:
1. Assume n=p^5. 1+p^5=5(p+p^2+p^3+p^4)=5p(1+p+p^2+p^3). That means p
| 1+p^5. This is not possible!
further refinement:
1. Assume n=p^5. 1+p^5=5(p+p^2+p^3+p^4)=5p(1+p+p^2+p^3). That means p
| 1+p^5. This is not possible!
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