Problem:
The remainder function can be defined for all real numbers x and y with yξ =0 by
rem(x,y)=xβyβyxββ
where βyxββ denotes the greatest integer less than or equal to yxβ. What is the value of rem(83β,β52β)?
Answer Choices:
A. β83β
B. β401β
C. 0
D. 83β
E. 4031β
Solution:
83ββ(β52β)β£β’β’β’β’β’ββ52β83βββ¦β₯β₯β₯β₯β₯β=83β+52βββ1615ββ=83β+52β(β1)=(B)β401ββ
The problems on this page are the property of the MAA's American Mathematics Competitions