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.
Study journal
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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