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Middle European Mathematical Olympiad
2019 Middle European Mathematical Olympiad
7
7
Part of
2019 Middle European Mathematical Olympiad
Problems
(1)
Divisibility inequality
Source: 2019 MEMO Problem T-7
8/30/2019
Let
a
,
b
a,b
a
,
b
and
c
c
c
be positive integers satisfying
a
<
b
<
c
<
a
+
b
a<b<c<a+b
a
<
b
<
c
<
a
+
b
. Prove that
c
(
a
−
1
)
+
b
c(a-1)+b
c
(
a
−
1
)
+
b
does not divide
c
(
b
−
1
)
+
a
c(b-1)+a
c
(
b
−
1
)
+
a
.Proposed by Dominik Burek, Poland
number theory
inequalities
MEMO 2019
memo