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2018 District Olympiad
1
{m/a} + {n/m} \ne 1
{m/a} + {n/m} \ne 1
Source: 2018 Romania District VIII p1
September 1, 2024
number theory
fractional part
Problem Statement
Prove that
{
m
n
}
+
{
n
m
}
≠
1
\left\{ \frac{m}{n}\right\}+\left\{ \frac{n}{m}\right\} \ne 1
{
n
m
}
+
{
m
n
}
=
1
, for any positive integers
m
,
n
m, n
m
,
n
.
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