Problem: For the natural numbers, when P is divided by D, the quotient is Q and the remainder is R. When Q is divided by Dβ², the quotient is Qβ² and the remainder is Rβ². Then, when P is divided by Dβ², the remainder is:
Answer Choices:
A. R+Rβ²D
B. Rβ²+RD
C. RRβ²
D. R
E. Rβ²
Solution:
P=QD+R and Q=Qβ²Dβ²+Rβ²β΄P=Qβ²DDβ²+Rβ²D+R, which means that when P is divided by Dβ² the quotient is Qβ² and the remainder is R+Rβ²D.