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Simon Marais Mathematical Competition
2024 Simon Marais Mathematical Competition
A1
Cyclic equalities involving floor.
Cyclic equalities involving floor.
Source: SMMC 2024 A1
October 12, 2024
algebra
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real number greater than 1 satisfying
⌊
a
⌋
b
=
⌊
b
⌋
c
=
⌊
c
⌋
a
.
\lfloor a\rfloor b = \lfloor b \rfloor c = \lfloor c\rfloor a.
⌊
a
⌋
b
=
⌊
b
⌋
c
=
⌊
c
⌋
a
.
Prove that
a
=
b
=
c
a=b=c
a
=
b
=
c
(Here,
⌊
x
⌋
\lfloor x \rfloor
⌊
x
⌋
denotes the laregst integer that is less than or equal to
x
x
x
.)
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