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4. Prove that if p is a prime number greater than 3, then p is of...

4. Prove that if p is a prime number greater than 3, then p is of the form 3k + 1 or 3k + 2.

5. Prove that if p is a prime number, then n √p is irrational for every integer n ≥ 2.

6. Prove or disprove that 3 is the only prime number of the form n2 −1.

7. Prove that if a is a positive integer of the form 3n+2, then at least one prime divisor of a is of the form 3n + 2.

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