Establish each of the following statements:
(a) Every integer of the form n4 + 4, with n > 1, is composite.
[Hint: Write n4 + 4 as a product of two quadratic factors.]
(b) If n > 4 is composite, then n divides (n − 1)!.
(c) Any integer of the form 8n + 1, where n ≥ 1, is composite.
[Hint: 2n + 1 | 23n + 1.]
(d) Each integer n > 11 can be written as the sum of two composite numbers.
[Hint: If n is even, say n=2k, then n−6−2(k − 3); for n odd, consider the integer n − 9.]
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.