Assignment:
Q1: Prove that there are no integers x, y, and z such that x^2 +y^2 + z^2 = 999
Q2: Show that square root of 2 cubed is an irrational number.
Q3: For each of the following pairs a and b, use the division algorithm to find quotient q and remainder r.
(a) b=189, a=17
(b) b=111, a= -5
(c) b= -1029, a=27
(d) b= -111, a= -4
Provide complete and step by step solution for the question and show calculations and use formulas.