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4
2005 Algebra #4: Floor Sum
2005 Algebra #4: Floor Sum
Source:
April 29, 2013
floor function
inequalities
function
search
algebra
Problem Statement
If
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
, what is the smallest possible value of
⌊
a
+
b
c
⌋
+
⌊
b
+
c
a
⌋
+
⌊
c
+
a
b
⌋
\left\lfloor \dfrac {a+b}{c} \right\rfloor + \left\lfloor \dfrac {b+c}{a} \right\rfloor + \left\lfloor \dfrac {c+a}{b} \right\rfloor
⌊
c
a
+
b
⌋
+
⌊
a
b
+
c
⌋
+
⌊
b
c
+
a
⌋
? (Note that
⌊
x
⌋
\lfloor x \rfloor
⌊
x
⌋
denotes the greatest integer less than or equal to
x
x
x
.)
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