1.State precisely what’s wrong with the proof of (FC-1). 2. Give a counterexample to (FC-1). 3. False Claim #2: 721 is prime. (FC-2) Bogus proof of (FC-2). In Example 4.8, we proved that n! + 1 is...

1.State precisely what’s wrong with the proof of (FC-1).

2. Give a counterexample to (FC-1).

3. False Claim #2: 721 is prime. (FC-2)

Bogus proof of (FC-2). In Example 4.8, we proved that n! + 1 is not evenly divisible by any k satisfying 2 ≤ k ≤ n. Observe that 6! = 720. Therefore, 721 = 6! + 1 isn’t evenly divisible by any integer between 2 and 720 inclusive, and therefore 721 is prime.

1.State precisely what’s wrong with the proof of (FC-2).

2.Without using a calculator, disprove (FC-2).

3.Without using a calculator, find an integer n such that n! + 1 is prime.