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Akdeniz University MO
1999 Akdeniz University MO
1
1
Part of
1999 Akdeniz University MO
Problems
(2)
number theory
Source:
1/31/2016
Prove that, we find infinite numbers such that, this number writeable
1999
k
+
1
1999k+1
1999
k
+
1
for
k
∈
N
k \in {\mathbb N}
k
∈
N
and all digits are equal.
number theory
number theory
Source:
1/31/2016
Let
n
n
n
's positive divisors sum is
T
(
n
)
T(n)
T
(
n
)
. For all
n
≥
3
n \geq 3
n
≥
3
's prove that,
(
T
(
n
)
)
3
<
n
4
(T(n))^3<n^4
(
T
(
n
)
)
3
<
n
4
number theory