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239 Open Math Olympiad
2021 239 Open Mathematical Olympiad
4
238^2 (ab)^{239} <1 if a^{239} = ac- 1 , b^{239} = bc- 1 for different a,b,c>0
238^2 (ab)^{239} <1 if a^{239} = ac- 1 , b^{239} = bc- 1 for different a,b,c>0
Source: 239 MO 2021 8-9 p4
May 2, 2021
algebra
inequalities
Problem Statement
Different positive
a
,
b
,
c
a, b, c
a
,
b
,
c
are such that
a
239
=
a
c
−
1
a^{239} = ac- 1
a
239
=
a
c
−
1
and
b
239
=
b
c
−
1
b^{239} = bc- 1
b
239
=
b
c
−
1
.Prove that
23
8
2
(
a
b
)
239
<
1
238^2 (ab)^{239} <1
23
8
2
(
ab
)
239
<
1
.
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