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Contests
National and Regional Contests
Turkey Contests
Turkey EGMO TST
2019 Turkey EGMO TST
4
4
Part of
2019 Turkey EGMO TST
Problems
(1)
NT about the positive divisors of n and n+1
Source: Turkey EGMO TST 2019 #4
7/15/2020
Let
σ
(
n
)
\sigma (n)
σ
(
n
)
shows the number of positive divisors of
n
n
n
. Let
s
(
n
)
s(n)
s
(
n
)
be the number of positive divisors of
n
+
1
n+1
n
+
1
such that for every divisor
a
a
a
,
a
−
1
a-1
a
−
1
is also a divisor of
n
n
n
. Find the maximum value of
2
s
(
n
)
−
σ
(
n
)
2s(n)- \sigma (n)
2
s
(
n
)
−
σ
(
n
)
.
number theory
number theory proposed