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Canada National Olympiad
1986 Canada National Olympiad
4
4
Part of
1986 Canada National Olympiad
Problems
(1)
Divisibility related to powers
Source: Canadian Mathematical Olympiad - 1986 - Problem 4.
7/3/2011
For all positive integers
n
n
n
and
k
k
k
, define
F
(
n
,
k
)
=
∑
r
=
1
n
r
2
k
−
1
F(n,k) = \sum_{r = 1}^n r^{2k - 1}
F
(
n
,
k
)
=
∑
r
=
1
n
r
2
k
−
1
. Prove that
F
(
n
,
1
)
F(n,1)
F
(
n
,
1
)
divides
F
(
n
,
k
)
F(n,k)
F
(
n
,
k
)
.
number theory unsolved
number theory