1 Prove the following statements a) There is a counting number n such that 2 n 7 n is a prime number b) Let a be an irrational number Then there exists an irrational number b such that ab is an integer

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1. Prove the following statements: a) There is a counting number n such that 2 n + 7 n is a prime number. b) Let

1. Prove the following statements:

a) There is a counting numbernsuch that 2ⁿ+ 7ⁿis a prime number.

b) Letabe an irrational number. Then there exists an irrational numberbsuch thatabis an integer.

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