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2023 Serbia National Math Olympiad
4
A number that never can be a power of q
A number that never can be a power of q
Source: Serbia MO 2023 P4
April 2, 2023
number theory
Problem Statement
Given a positive integer
n
n
n
and a prime
q
q
q
, prove that the number
n
q
+
(
n
−
1
2
)
2
n^q+(\frac{n-1}{2})^2
n
q
+
(
2
n
−
1
)
2
can't be a power of
q
q
q
.
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