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STEMS 2022 Math Cat A Qualifier Round
2
tRiCkY NuMbEr ThEoRy
tRiCkY NuMbEr ThEoRy
Source: STEMS 2021-22 Math CatA Q 2
December 19, 2021
number theory
Problem Statement
Define a function
g
:
N
→
R
g :\mathbb{N} \rightarrow \mathbb{R}
g
:
N
→
R
Such that
g
(
x
)
=
4
x
+
4
x
+
1
+
4
x
+
2
+
.
.
.
g(x)=\sqrt{4^x+\sqrt {4^{x+1}+\sqrt{4^{x+2}+...}}}
g
(
x
)
=
4
x
+
4
x
+
1
+
4
x
+
2
+
...
. Find the last 2 digits in the decimal representation of
g
(
2021
)
g(2021)
g
(
2021
)
.
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