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p, p^2 + 2 prime => p^3+2 prime

Problem:
Show that if p and p^2 +2 are prime, then so is p^3 + 2 .

Solution:
p can't be 2.
For p = 3 , the statement is true.
If p > 3, we know that p^2 = 1 \pmod 3 . Hence p^2 + 2 is always divisible by 3.
QED.

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