Problem:
Let a0=2,a1=5, and a2=8, and for n>2 define an recursively to be the remainder when 4(an−1+an−2+an−3) is divided by 11 . Find a2018⋅a2020⋅a2022.
Solution:
Calculating the first few values of ak shows that they repeat with period 10 and a8=7. It follows that a2018⋅a2020⋅a2022=a8⋅a0⋅a2=7⋅2⋅8=112.
The problems on this page are the property of the MAA's American Mathematics Competitions