Anomalous Cancellation/Variants/3 + 25 + 38 over 7 + 20 + 39

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Theorem

$\dfrac {3 + 25 + 38} {7 + 20 + 39} = \dfrac {3^4 + 25^4 + 38^4} {7^4 + 20^4 + 39^4}$


Proof

\(\displaystyle \dfrac {3^4 + 25^4 + 38^4} {7^4 + 20^4 + 39^4}\) \(=\) \(\displaystyle \dfrac {81 + 390625 + 2085136} {2401 + 160000 + 2313441}\)
\(\displaystyle \) \(=\) \(\displaystyle \dfrac {2475842} {2475842}\)


\(\displaystyle \dfrac {3 + 25 + 38} {7 + 20 + 39}\) \(=\) \(\displaystyle \dfrac {66} {66}\)
\(\displaystyle \) \(=\) \(\displaystyle \dfrac {2475842} {2475842}\)

$\blacksquare$


Sources