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MathLinks Contest 5th
6.2
6.2
Part of
MathLinks Contest 5th
Problems
(1)
0562 number theory 5th edition Round 6 p2
Source:
5/6/2021
We say that a positive integer
n
n
n
is nice if
4
n
\frac{4}{n}
n
4
cannot be written as
1
x
+
1
x
y
+
1
z
\frac{1}{x}+\frac{1}{xy}+\frac{1}{z}
x
1
+
x
y
1
+
z
1
for any positive integers
x
,
y
,
z
x, y, z
x
,
y
,
z
. Let us denote by
a
n
a_n
a
n
the number of nice numbers smaller than
n
n
n
. Prove that the sequence
n
a
n
\frac{n}{a_n}
a
n
n
is not bounded.
number theory
5th edition