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
\(\ds \dfrac {3^4 + 25^4 + 38^4} {7^4 + 20^4 + 39^4}\) | \(=\) | \(\ds \dfrac {81 + 390625 + 2085136} {2401 + 160000 + 2313441}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {2475842} {2475842}\) |
\(\ds \dfrac {3 + 25 + 38} {7 + 20 + 39}\) | \(=\) | \(\ds \dfrac {66} {66}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {2475842} {2475842}\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $16 / 64$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $16 / 64$