Question

If E(0), E(1),..., E(n-1) are the pth roots of unity for p a prime then it is true that

Answer 1

If E(0), E(1),..., E(n-1) are the pth roots of unity for p a prime, then it is true that they satisfy the equation E(0) + E(1) + ... + E(n-1) = 0.

Step-by-step explanation:

If E(0), E(1),..., E(n-1) are the pth roots of unity for p a prime, then it is true that they satisfy the equation E(0) + E(1) + ... + E(n-1) = 0.

To prove this, let's consider the case where p = 2 and n = p. We have E(0) + E(1) = 0, which is true because the only two pth roots of unity are 1 and -1, and their sum is indeed 0.

This result can be extended to any prime number p and any positive integer n.