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1. Find q and r as defined in the Division Algorithm when a = 549 and b = 236
2. Suppose N > 1 is a natural number and f: Z →N υ {0} is the function that associates with each a ε Z its remainder upon division by n; thus, if a = qn + r with 0 ≤ r < n, then f(a) = r.
(a.) Find the domain and range of f
(b.) Is f one-to-one?
(c.) Is f onto?
3. Find the binary, octal and hexadecimal representations for 2705.
4. Let Sbe the set of all people in the world. For a, b ε S, define a binary relation R as follows: (a, b) ε R if and only if a and b have visited the same webpage. Is this an example of a partially ordered set? Why or why not?
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For RSA signature, let p=17 and q=43. Design a digital signature for the message m=161, where the hashing function is the identity function and the computation at the signer's side is performed through the Chinese Remainder Theory.
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