Amicable Pair/Examples/10,744-10,856

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Example of Amicable Pair

$10 \, 744$ and $10 \, 856$ are the $6$th amicable pair:

$\sigma \left({10 \, 744}\right) = \sigma \left({10 \, 856}\right) = 21 \, 600 = 10 \, 744 + 10 \, 856$


Proof

By definition, $m$ and $n$ form an amicable pair if and only if:

$\sigma \left({m}\right) = \sigma \left({n}\right) = m + n$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function.


Thus:

\(\displaystyle \sigma \left({10 \, 744}\right)\) \(=\) \(\displaystyle 21 \, 600\) $\sigma$ of $10 \, 744$
\(\displaystyle \) \(=\) \(\displaystyle 10 \, 744 + 10 \, 856\)
\(\displaystyle \) \(=\) \(\displaystyle \sigma \left({10 \, 856}\right)\) $\sigma$ of $10 \, 856$

$\blacksquare$


Sources