MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P13
P13
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Standard technique power NT
Source: Latvia BW TST 2021 P13
9/26/2021
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?
number theory