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2020 BMT Fall
5
BMT Algebra #5 - Functional Equation
BMT Algebra #5 - Functional Equation
Source:
October 11, 2020
Bmt
algebra
function
functional equation
Problem Statement
Let
f
:
R
+
→
R
+
f:\mathbb{R}^+\to \mathbb{R}^+
f
:
R
+
→
R
+
be a function such that for all
x
,
y
∈
R
+
,
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
x
y
)
x,y \in \mathbb{R}+,\, f(x)f(y)=f(xy)+f\left(\frac{x}{y}\right)
x
,
y
∈
R
+
,
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
f
(
y
x
)
, where
R
+
\mathbb{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\left(2^{2^{2020}}\right)
f
(
2
2
2020
)
.
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