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Problems
Contests
National and Regional Contests
PEN Problems
PEN J Problems
17
17
Part of
PEN J Problems
Problems
(1)
J 17
Source:
5/25/2007
Show that
ϕ
(
n
)
+
σ
(
n
)
≥
2
n
\phi(n)+\sigma(n) \ge 2n
ϕ
(
n
)
+
σ
(
n
)
≥
2
n
for all positive integers
n
n
n
.
function
number theory
totient function
Divisor Functions