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Kosovo National Mathematical Olympiad
2017 Kosovo National Mathematical Olympiad
1
Kosovo National MO Grade 11.
Kosovo National MO Grade 11.
Source:
July 16, 2017
number theory
Problem Statement
Find all ordered pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
, of natural numbers, where
1
<
a
,
b
≤
100
1<a,b\leq 100
1
<
a
,
b
≤
100
, such that
1
log
a
10
+
1
log
b
10
\frac{1}{\log_{a}{10}}+\frac{1}{\log_{b}{10}}
l
o
g
a
10
1
+
l
o
g
b
10
1
is a natural number.
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