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KoMaL A Problems
KoMaL A Problems 2018/2019
A. 751
A. 751
Part of
KoMaL A Problems 2018/2019
Problems
(1)
Powers are integers
Source:
5/12/2019
Let
c
>
0
c>0
c
>
0
be a real number, and suppose that for every positive integer
n
n
n
, at least one percent of the numbers
1
c
,
2
c
,
⋯
,
n
c
1^c, 2^c, \cdots , n^c
1
c
,
2
c
,
⋯
,
n
c
are integers. Prove that
c
c
c
is an integer.
number theory