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Latvia BW TST
2021 Latvia Baltic Way TST
P13
Standard technique power NT
Standard technique power NT
Source: Latvia BW TST 2021 P13
September 26, 2021
number theory
Problem Statement
Does there exist a natural number
a
a
a
so that: a)
(
(
a
2
−
3
)
3
+
1
)
a
−
1
\Big ((a^2-3)^3+1\Big) ^a-1
(
(
a
2
−
3
)
3
+
1
)
a
−
1
is a perfect square? b)
(
(
a
2
−
3
)
3
+
1
)
a
+
1
−
1
\Big ((a^2-3)^3+1\Big) ^{a+1}-1
(
(
a
2
−
3
)
3
+
1
)
a
+
1
−
1
is a perfect square?
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