# COT 3100H Spring 2008 Homework #7 Assigned: 3/4/08 (Tuesday) Due: 3/6/08 (Thursday) ```COT 3100H Spring 2008 Homework #7
Assigned: 3/4/08 (Tuesday)
Due: 3/6/08 (Thursday)
1) Find GCD(729, 321) using Euclid's Algorithm.
2) Find all integer solutions for x and y to the equation 729x + 321y = gcd(729, 321).
3) Find all integer solutions for x and y to the equation 729x + 321y = 36.
4) What is the least common multiple of 729 and 321?
5) Prove that
3 is irrational.
6) Determine the number of positive integer divisors of 2534108.
7) Determine the sum of the divisors in question #6.
8) Prove that the fourth power of an odd integer leaves a remainder of 1 when divided by
16. (Hint: You may want to first prove that the expression a(a+1) or a(3a+1) is even for
all integers a.)
Programming Option: Write a program that automatically prints out all the steps of
Euclid's Algorithm in an easy to read format. It should prompt the user for the two values
for the GCD calcuation. If you do this question, you can skip questions #1, 2 and 3.
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