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Sweden Contests
Swedish Mathematical Competition
1989 Swedish Mathematical Competition
1
1
Part of
1989 Swedish Mathematical Competition
Problems
(1)
n^2(n^2 + 2)^2 , n^4(n^2 + 2)^2, in base n^2 +1, same digits
Source: 1989 Swedish Mathematical Competition p1
3/28/2021
Let
n
n
n
be a positive integer. Prove that the numbers
n
2
(
n
2
+
2
)
2
n^2(n^2 + 2)^2
n
2
(
n
2
+
2
)
2
and
n
4
(
n
2
+
2
)
2
n^4(n^2 + 2)^2
n
4
(
n
2
+
2
)
2
are written in base
n
2
+
1
n^2 +1
n
2
+
1
with the same digits but in opposite order.
number theory
Digits
Perfect Square