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2013 BMT Spring
4
BMT 2013 Spring - Discrete 4
BMT 2013 Spring - Discrete 4
Source:
January 6, 2022
number theory
algebra
Problem Statement
Given
f
1
(
x
)
=
2
x
−
2
f_1(x)=2x-2
f
1
(
x
)
=
2
x
−
2
and, for
k
≥
2
k\ge2
k
≥
2
, defined
f
k
(
x
)
=
f
(
f
k
−
1
(
x
)
)
f_k(x)=f(f_{k-1}(x))
f
k
(
x
)
=
f
(
f
k
−
1
(
x
))
to be a real-valued function of
x
x
x
. Find the remainder when
f
2013
(
2012
)
f_{2013}(2012)
f
2013
(
2012
)
is divided by the prime
2011
2011
2011
.
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