Prove each of the assertions below:
(a) Any prime of the form 3n + 1 is also of the form 6m + 1.
(b) Each integer of the form 3n + 2 has a prime factor of this form.
(c) The only prime of the form n3 − 1 is 7.
[Hint: Write n3 − 1 as (n− 1 )(n2 + n + 1).]
(d) The only prime p for which 3p + 1 is a perfect square is p = 5.
(e) The only prime of the form n2 − 4 is 5.
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