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2020 BMT Fall
25
2020 BMT Individual 25
2020 BMT Individual 25
Source:
January 9, 2022
number theory
Problem Statement
Let
f
:
R
+
→
R
+
f : R^+ \to R^+
f
:
R
+
→
R
+
be a function such that for all
x
,
y
∈
R
+
x, y \in R^+
x
,
y
∈
R
+
,
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
y
)
f(x)f(y) = f(xy) + f\left( \frac{x}{y}\right)
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
y
x
)
, where
R
+
R^+
R
+
represents the positive real numbers. Given that
f
(
2
)
=
3
f(2) = 3
f
(
2
)
=
3
, compute the last two digits of
f
(
2
2
2020
)
f(2^{2^{2020}})
f
(
2
2
2020
)
. .
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