Question 1
Consider the following two Diophantine equations with integervariables X and Y
(1) 99 X + 225 Y = 36
(2) 225 X + 99 Y = 33
(a) Determine which of these two equations is inconsistent, andexplain why
(you can use the Maple commands ifactor and/or gcd ).
For the equation that is consistent, apply Extended Euclid'sAlgorithm to find a solution  {X0, Y0}
.
(b) Find now all solutions  {X, Y} of that equation,and identify the solution with smallest possible absolute valueof  Y
. Â
QUESTION 2
Consider the ring of congruence classes R=?/15?:
(a) Identify the set S of all zero divisors and the set U of allunits in R. Explain your solution.
(b) For the element [10], find all complementary zero divisorsor all inverses, whichever exists. Explain.
(c) Find all solutions of the equation [23] X = [12]
if it is consistent, or explain why this equation isinconsistent.
