2020 AIME II Problems/Problem 6
Problem
Define a sequence recursively by ,
, and
for all
. Then
can be written as
, where
and
are relatively prime positive integers. Find
.
Solution
Let . Then, we have
where
and
. By substitution, we find
,
,
,
, and
. So
has a period of
. Thus
. So,
.
~mn28407
Video Solution
https://youtu.be/_JTWJxbDC1A ~ CNCM
Video Solution 2
~IceMatrix
See Also
2020 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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