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Tuymaada Olympiad
2019 Tuymaada Olympiad
6
Prove that expression is not square of a natural number
Prove that expression is not square of a natural number
Source: Tuymaada 2019 P6 out of 8
July 15, 2019
number theory
square
Tuymaada
Problem Statement
Prove that the expression
(
1
4
+
1
2
+
1
)
(
2
4
+
2
2
+
1
)
…
(
n
4
+
n
2
+
1
)
(1^4+1^2+1)(2^4+2^2+1)\dots(n^4+n^2+1)
(
1
4
+
1
2
+
1
)
(
2
4
+
2
2
+
1
)
…
(
n
4
+
n
2
+
1
)
is not square for all
n
∈
N
n \in \mathbb{N}
n
∈
N
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