Smallest Seventh Power which is Sum of 8 other Seventh Powers

Theorem

The smallest seventh power that can be expressed as the sum of $8$ other seventh powers is $102^7$:

$102^7 = 12^7 + 35^7 + 53^7 + 58^7 + 64^7 + 83^7 + 85^7 + 90^7$

Proof

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $102$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $102$