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Kvant 2022
M2707
M2707
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Kvant 2022
Problems
(1)
Representation in sum of fractions
Source: VII Caucasus Mathematical Olympiad
3/13/2022
Prove that infinitely many positive integers can be represented as
(
a
−
1
)
/
b
+
(
b
−
1
)
/
c
+
(
c
−
1
)
/
a
(a-1)/b + (b-1)/c + (c-1)/a
(
a
−
1
)
/
b
+
(
b
−
1
)
/
c
+
(
c
−
1
)
/
a
, where
a
a
a
,
b
b
b
and
c
c
c
are pairwise distinct positive integers greater than 1.
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