UCF Computer Science



CIS 3362 Homework #5 Solution

Number Theory, RSA

Due: Wednesday, 11/10/2010

1) Determine the following values:

a) Φ(235) = Φ(5 x 47) = (5 – 1)(47 – 1) = 184

b) Φ(5045) = Φ(5 x 1009) = (5 – 1)(1009 – 1) = 4032

c) Φ(6034176) = Φ(28 x 35 x 97) = (28 – 27)(35 – 34)(97 – 1) = 1990656

d) Φ(646000000) = Φ(27 x 56 x 17 x 19) = (27 – 26)(56 – 55)(17 – 1)(19 – 1) = 230400000

e) Φ(55898489) = Φ(7129 x 7841) = (7129 – 1)(7841 – 1) = 55883520

Note: A calculator was used to prime factorize (a) through (d), but the program below was used to prime factorize (e):

#include

int main() {

int val = 55898489; // Hard-coded for problem 1e.

int div = 2;

while (div ................
................

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