MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN J Problems
4
J 4
J 4
Source:
May 25, 2007
algebra
polynomial
arithmetic sequence
Divisor Functions
Problem Statement
Let
m
m
m
,
n
n
n
be positive integers. Prove that, for some positive integer
a
a
a
, each of
ϕ
(
a
)
\phi(a)
ϕ
(
a
)
,
ϕ
(
a
+
1
)
\phi(a+1)
ϕ
(
a
+
1
)
,
⋯
\cdots
⋯
,
ϕ
(
a
+
n
)
\phi(a+n)
ϕ
(
a
+
n
)
is a multiple of
m
m
m
.
Back to Problems
View on AoPS