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Korea Junior Mathematics Olympiad
2006 Korea Junior Math Olympiad
2
2
Part of
2006 Korea Junior Math Olympiad
Problems
(1)
b/a+c/a+c/b+a/b+a/c+b/c is an pos. integer, where a,b,c coprime pos. integers
Source: KJMO 2006 p2
5/1/2019
Find all positive integers that can be written in the following way
b
a
+
c
a
+
c
b
+
a
b
+
a
c
+
b
c
\frac{b}{a}+\frac{c}{a}+\frac{c}{b}+\frac{a}{b}+\frac{a}{c}+\frac{b}{c}
a
b
+
a
c
+
b
c
+
b
a
+
c
a
+
c
b
. Also,
a
,
b
,
c
a,b, c
a
,
b
,
c
are positive integers that are pairwise relatively prime.
number theory
coprime
positive integers
Integers