1. Let k points z_1, z_2, ... z_k be given in the plane of complex numbers, and let a_1, a_2, ... a_k be nonnegative numbers, for which a1 + a2 + ... + a_k = 1. Then the number, y = a_1*z_1 + a_2*z_2 + ... + a_k*z_k lies in the smallest convex (closed) polygon containing the points z_1, z_2, ... z_k.
Is this still true for infinite sequences {z_n} and {z_n}, provided that \sum a_n = 1 and \sum a_n*z_n = y exists?
Name:
Anonymous2012-10-27 11:28
>>7
[Brouwer mode]
No. Nothing is true for infinite sequences since we can't extrapolate rules that we apply to finite sequences.
[/Brouwer mode]
Name:
Anonymous2012-10-27 11:33
2. Create or cite a public/private key encryption algorithm that allows one to encrypt a message so that it may then be received and decoded by n other known recipients. That is, given the public keys of the recipients, p_1, p_2, ... p_n, and a plain text, P, create a cipher text C such that P can be recovered from C if at least one of the private keys, k_1, k_2, ... k_n, are known.
C = Encrpyt(P, (p_1, p_2, ... p_n))
P = Decrypt(P, k_i) for each i
Name:
Anonymous2012-10-27 11:48
>>9
There are at least two simple algorithms: one uses hypersurfaces, the other uses polynomial functions.
Boring.