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National and Regional Contests
Greece Contests
Greece JBMO TST
1998 Greece JBMO TST
5
5
Part of
1998 Greece JBMO TST
Problems
(1)
Greece TST 1998 Q5
Source:
3/11/2013
Let
I
I
I
be an open interval of length
1
n
\frac{1}{n}
n
1
, where
n
n
n
is a positive integer. Find the maximum possible number of rational numbers of the form
a
b
\frac{a}{b}
b
a
where
1
≤
b
≤
n
1 \le b \le n
1
≤
b
≤
n
that lie in
I
I
I
.
ceiling function
algebra unsolved
algebra